81:
71:
53:
2309:
22:
203:
161:
137:
2897:
is, like stochastic programming, an attempt to capture uncertainty in the data underlying the optimization problem. This is not done through the use of random variables, but instead, the problem is solved taking into account inaccuracies in the input
2934:
make few or no assumptions about the problem being optimized. Usually, heuristics do not guarantee that any optimal solution need be found. On the other hand, heuristics are used to find approximate solutions for many complicated optimization
2880:
studies the general case in which the objective function or the constraints or both contain nonlinear parts. This may or may not be a convex program. In general, whether the program is convex affects the difficulty of solving
2867:
allows the objective function to have quadratic terms, while the feasible set must be specified with linear equalities and inequalities. For specific forms of the quadratic term, this is a type of convex
2987:
studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems. The equation that describes the relationship between these subproblems is called the
264:
2206:
3363:
alphaBB, AlphaECP, AOA, BARON, BNB, BONMIN, Couenne, DICOPT, Xpress-SLP, FILMINT, FMINCONSET, KNITRO, LAGO, LINDOBB, LINDOGlobal, LOGMIP, MIDACO, MILANO, MINLP_BB, MISQP, OQNLP, SBB
2994:
2077:
1856:
1779:
2201:
2975:
seeks to optimize an objective defined over many points in time, by considering how the objective function changes if there is a small change in the choice path.
2874:
studies optimization of ratios of two nonlinear functions. The special class of concave fractional programs can be transformed to a convex optimization problem.
3511:
1080:
250:
237:
3531:
3536:
3521:
3516:
103:
3526:
2215:
2695:
177:
2070:
3352:
Interior-Point LP Solvers: BPMPD, CLP, FortMP, GIPALS32, HOPDM, GLPK, CPLEX, LINDO, LIPSOL, LOQO, MSF, MOSEK, PCx, SAS/OR, Xpress-Optimizer
2968:
In a number of subfields, the techniques are designed primarily for optimization in dynamic contexts (that is, decision making over time):
2800:– This can be viewed either as a particular case of nonlinear programming or as generalization of linear or convex quadratic programming.
94:
58:
2776:
2238:
2036:
3289:
2151:
2258:
212:
147:
2917:
365:
2964:
Disjunctive programming is used where at least one constraint must be satisfied but not all. It is of particular use in scheduling.
168:
142:
2290:
2835:
is a general form of convex programming. LP, SOCP and SDP can all be viewed as conic programs with the appropriate type of cone.
2369:
2063:
2050:
3391:
Quadratically
Constrained Quadratic Programming (QCQP) / Mixed Integer Quadratically Constrainted Quadratic Programming (MIQCQP)
3541:
33:
3546:
2646:
2308:
2813:
2754:
2374:
2029:
1691:
1379:
1253:
1225:
606:
2690:
2658:
2927:
1929:
1758:
1445:
1351:
1048:
974:
921:
880:
818:
813:
774:
626:
413:
385:
3355:
Conic
Optimization Software: CPLEX, CSDP, CVXOPT, DSDP, LMIlab, LOQO, MOSEK, PENSDP, SDPA, SDPlr, SDPT3, SeDuMi, SMCP
2739:
2364:
1668:
1245:
2685:
2641:
2243:
2901:
2534:
936:
739:
698:
588:
485:
370:
2424:
1972:
1415:
1410:
1162:
520:
470:
465:
2789:
2086:
1924:
1722:
273:
3339:
1177:
1053:
992:
885:
706:
639:
545:
3406:
Nonlinear
Programming (NLP) / Mixed Integer Nonlinear Programming (MINLP) / Global Nonlinear Programming (GNLP)
2998:
2819:
2263:
1383:
39:
2946:
2938:
2911:
2609:
2552:
2268:
3021:
2146:
3002:
2972:
2956:
2884:
2871:
2744:
2729:
2497:
2471:
2123:
2090:
1957:
654:
2877:
2864:
2838:
2653:
2633:
2599:
2502:
2444:
2325:
2131:
2111:
1838:
1544:
1527:
1496:
1303:
1099:
1090:
1076:
900:
442:
325:
176:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
102:
on
Knowledge (XXG). If you would like to participate, please visit the project page, where you can join
80:
3368:
CONOPT, FilterSQP, KNITRO, LINDO LRAMBO, NLPQLP, NPSOL, PATHNLP, SNOPT, SQPlab; <ALM Solvers: -->
2619:
1509:
1475:
1356:
1182:
1058:
997:
890:
787:
644:
550:
3378:
2905:
2826:
2419:
1799:
3358:
MILP software: CPLEX, Gurobi, LINDO, MOSEK, Xpress-Optimizer, BLIS, CBC, GLPK, MINTO, SCIP, SYMPHONY
2055:
2984:
2950:
2894:
2854:
2749:
2567:
2557:
2409:
2397:
2210:
2193:
2098:
1613:
1570:
1430:
1152:
1007:
510:
2904:
is concerned with problems where the set of feasible solutions is discrete or can be reduced to a
403:
2803:
2796:
2680:
2507:
2484:
2453:
2439:
2429:
2220:
2012:
433:
423:
86:
3374:
2861:
values. This is not convex, and in general much more difficult than regular linear programming.
2810:
is linear and the set of constraints is specified using only linear equalities and inequalities.
1939:
1817:
1763:
1658:
1361:
1235:
70:
52:
2614:
1919:
1608:
1598:
1425:
1346:
1147:
1035:
951:
872:
754:
598:
505:
2832:
2492:
2170:
1901:
1846:
1807:
1717:
1686:
1676:
1450:
1264:
560:
480:
1881:
1748:
1681:
1638:
1326:
979:
779:
631:
540:
2988:
2572:
2562:
2466:
2343:
2248:
2230:
2183:
2136:
2094:
1896:
1876:
1866:
1812:
1789:
1784:
1743:
1712:
1696:
1648:
1618:
1593:
1575:
1470:
1440:
1043:
969:
797:
769:
685:
672:
621:
535:
408:
360:
3394:
Second-order cone programming (SOCP) / Mixed
Integer Second-order cone programming (MISOCP)
1914:
1909:
1623:
1552:
1465:
1460:
1230:
1220:
1172:
1112:
1107:
616:
568:
495:
450:
300:
3494:
3489:
2978:
2888:
2588:
1455:
1205:
1167:
844:
525:
315:
305:
3411:
2914:
for use with random (noisy) function measurements or random inputs in the search process.
530:
3340:
Wiley
Encyclopedia of Operations Research and Management Science: Optimization Software
2576:
2461:
2348:
2282:
2253:
1990:
716:
3476:
3505:
3165:
2931:
2806:(LP), a type of convex programming, studies the case in which the objective function
2734:
2718:
2003:
242:
202:
2823:
2672:
2178:
310:
290:
3366:
Software for
Nonlinearly Constrained Optimization: <Interior-Point Solvers: -->
2857:
studies linear programs in which some or all variables are constrained to take on
3481:
2842:
2759:
2141:
295:
99:
2920:
studies the case when the set of feasible solutions is a subset of an infinite-
160:
136:
3161:
2822:(SDP) is a subfield of convex optimization where the underlying variables are
1585:
1192:
76:
2816:(SOCP) is a convex program, and includes certain types of quadratic programs.
2921:
2846:
344:
2887:
studies the case in which some of the constraints or parameters depend on
3022:
Mathematical
Programming Glossary: The Nature of Mathematical Programming
2841:
is a technique whereby objective and inequality constraints expressed as
2161:
1851:
173:
3367:
Ipfilter, IPOPT, KNITRO, LANCELOT, LINDO, LOQO; <SLP/SQP Solvers: -->
3471:
3461:
3388:
Quadratic
Programming (QP) / Mixed Integer Quadratic Programming (MIQP)
2858:
2481:
1871:
1311:
1210:
1117:
1015:
987:
916:
911:
852:
823:
808:
724:
573:
455:
398:
1982:
1891:
1886:
1753:
1628:
1603:
1565:
1420:
1341:
1331:
1321:
1282:
1277:
1215:
1142:
1132:
1127:
1030:
1025:
946:
941:
931:
867:
862:
749:
744:
734:
693:
593:
583:
500:
490:
475:
390:
3102:
3466:
2829:. It is generalization of linear and convex quadratic programming.
1977:
1934:
1861:
1738:
1653:
1643:
1633:
1560:
1504:
1435:
1405:
1336:
1316:
1272:
1200:
1157:
1137:
1122:
1020:
964:
959:
926:
857:
764:
759:
729:
667:
662:
611:
578:
515:
460:
380:
375:
352:
334:
3385:
Linear Programming (LP) / Mixed Integer Linear Programming (MILP)
339:
2716:
2532:
2395:
2323:
2109:
2059:
246:
3103:
Decision Tree for Optimization Software: Problems and Software
15:
3362:
CPLEX, Xpress-Optimizer, MOSEK, SCIP; <General MINLP: -->
2307:
201:
2981:
theory is a generalization of the calculus of variations.
3482:
OR/MS Today: 1998 Nonlinear Programming Software Survey
3270:
Mathematical Programs with Complementarity Constraints
3258:
Complementarity Problems and Variational Inequalities
2995:
Mathematical programming with equilibrium constraints
3477:
OR/MS Today: 2013 Linear Programming Software Survey
3290:
Optimization Software Guide: Software Classification
172:, a collaborative effort to improve the coverage of
98:, a collaborative effort to improve the coverage of
2671:
2632:
2598:
2587:
2545:
2480:
2452:
2438:
2408:
2357:
2336:
2281:
2229:
2192:
2169:
2160:
2122:
2002:
1956:
1837:
1830:
1798:
1772:
1731:
1705:
1667:
1584:
1543:
1536:
1526:
1495:
1488:
1399:
1392:
1378:
1302:
1295:
1262:
1244:
1191:
1098:
1089:
1075:
1006:
899:
843:
836:
796:
715:
684:
653:
559:
441:
432:
422:
324:
280:
3273:Mathematical Programs with Equilibrium Constraints
3196:Quadratic Constrained Quadratic Programming (QCQP)
3144:Least Squares: Unconstrained LSQ, Constrained LSQ
2941:studies the case in which the objective function
3467:NEOS Optimization Guide: Linear Programming FAQ
32:does not require a rating on Knowledge (XXG)'s
231:Alternative taxonomies for math. opt. software
3472:Optimization Guide: Nonlinear Programming FAQ
2071:
258:
8:
3421:Complementarity and Variational Inequalities
3230:Mixed Integer Nonlinear Programming (MILNP)
238:Template:Mathematical optimization software
3445:Optimization Software and Modeling Systems
3369:ALGENCAN, GALAHAD, LANCELOT, MINOS, PENNON
3162:NEOS Optimization Guide: Optimization Tree
2713:
2629:
2595:
2542:
2529:
2449:
2405:
2392:
2333:
2320:
2166:
2119:
2106:
2078:
2064:
2056:
1834:
1540:
1533:
1492:
1396:
1389:
1299:
1095:
1086:
840:
438:
429:
265:
251:
243:
131:
47:
3436:Linear, Cone and Semidefinite Programming
2849:can be transformed into a convex program.
2790:Mathematical optimization#Major subfields
2312:Optimization computes maxima and minima.
133:
112:Knowledge (XXG):WikiProject Mathematics
49:
3412:Optimization Online Submissions: Areas
3139:Dynamic Programming / Control Problems
2508:Principal pivoting algorithm of Lemke
166:This template is within the scope of
92:This template is within the scope of
21:
19:
7:
3400:System of Nonlinear Equations (SNLE)
3202:Second Order Cone Programming (SOCP)
2924:space, such as a space of functions.
186:Knowledge (XXG):WikiProject Software
3512:Template-Class mathematics articles
3462:NEOS Optimization Guide: Algorithms
2037:Comparison of optimization software
38:It is of interest to the following
3276:Nonlinear Complementarity Problems
2152:Successive parabolic interpolation
274:Mathematical optimization software
14:
3532:Template-Class Computing articles
3430:Infinite Dimensional Optimization
3424:Convex and Nonsmooth Optimization
3227:Integer Linear Programming (ILP)
2997:is where the constraints include
2918:Infinite-dimensional optimization
2472:Projective algorithm of Karmarkar
3537:NA-importance Computing articles
3522:Template-Class software articles
3517:NA-priority mathematics articles
3238:Traveling Salesman Problem (TSP)
3235:Combinatorial Optimization (CO)
2467:Ellipsoid algorithm of Khachiyan
2370:Sequential quadratic programming
2207:Broyden–Fletcher–Goldfarb–Shanno
2051:Template:Optimization algorithms
159:
135:
115:Template:WikiProject Mathematics
79:
69:
51:
20:
3527:NA-importance software articles
3267:Linear Complementarity Problems
3245:Optimization Under Uncertainty
3397:Semidefinite Programming (SDP)
3361:MINLP software: <MIQCP: -->
3329:Multiple Criteria Optimization
3326:Nondifferentiable Optimization
3311:Bound Constrained Optimization
3214:Nonlinear Least Squares (NLLS)
3208:Semiinfinite Programming (SIP)
3205:Semidefinite Programming (SDP)
3190:Nondifferentiable Optimization
3175:Bound Constrained Optimization
2425:Reduced gradient (Frank–Wolfe)
210:This template is supported by
1:
3486:Arnold Neumaier's catalog of
3403:Nonlinear Least Squares (NLS)
3251:Stochastic Linear Programming
2945:is constant (this is used in
2814:Second order cone programming
2755:Spiral optimization algorithm
2375:Successive linear programming
2030:List of optimization software
189:Template:WikiProject Software
180:and see a list of open tasks.
106:and see a list of open tasks.
3490:Global Optimization Software
3181:Derivative-Free Optimization
3013:Multi-objective optimization
2845:and equality constraints as
2493:Simplex algorithm of Dantzig
2365:Augmented Lagrangian methods
3495:Local Optimization Software
3281:Multiobjective Optimization
3211:Unconstrained Optimization
3193:Nonlinear Programming (NLP)
3150:Multiobjective Optimization
3563:
3418:Combinatorial Optimization
3296:Unconstrained Optimization
3199:Quadratic Programming (QP)
3112:Unconstrained Optimization
2902:Combinatorial optimization
3115:Constrained Optimization
2772:
2725:
2712:
2696:Push–relabel maximum flow
2541:
2528:
2498:Revised simplex algorithm
2404:
2391:
2332:
2319:
2305:
2118:
2105:
2024:
209:
154:
64:
46:
3349:Simplex-based LP Solvers
3314:Constrained Optimization
3261:Complementarity Problems
3178:Constrained Optimization
3172:Continuous Optimization
3016:Multi-modal optimization
2999:variational inequalities
2820:Semidefinite programming
2221:Symmetric rank-one (SR1)
2202:Berndt–Hall–Hall–Hausman
3299:Nonlinear Least Squares
3248:Stochastic Programming
3187:Linear Programming (LP)
2947:artificial intelligence
2939:Constraint satisfaction
2912:Stochastic optimization
2745:Parallel metaheuristics
2553:Approximation algorithm
2264:Powell's dog leg method
2216:Davidon–Fletcher–Powell
2112:Unconstrained nonlinear
95:WikiProject Mathematics
3542:All Computing articles
3451:Stochastic Programming
3442:Nonlinear Optimization
3224:Discrete Optimization
3136:Constraint Programming
2973:Calculus of variations
2957:Constraint programming
2885:Stochastic programming
2872:Fractional programming
2730:Evolutionary algorithm
2313:
206:
3547:All Software articles
3375:OPTI Toolbox: Solvers
3308:Quadratic Programming
3153:Discrete Optimization
3127:Geometric programming
2878:Nonlinear programming
2865:Quadratic programming
2839:Geometric programming
2503:Criss-cross algorithm
2326:Constrained nonlinear
2311:
2132:Golden-section search
236:Extensive version of
213:WikiProject Computing
205:
3439:Network Optimization
3317:Network Optimization
3133:Network Optimization
2420:Cutting-plane method
169:WikiProject Software
118:mathematics articles
3448:Robust Optimization
3433:Integer Programming
3427:Global Optimization
3320:Integer Programming
3302:Nonlinear Equations
3217:Nonlinear Equations
3184:Global Optimization
3166:NEOS Solvers: Index
3109:Global Optimization
2985:Dynamic programming
2951:automated reasoning
2855:Integer programming
2750:Simulated annealing
2568:Integer programming
2558:Dynamic programming
2398:Convex optimization
2259:Levenberg–Marquardt
1178:XA Quadratic Solver
3456:Other useful links
3305:Linear Programming
2949:, particularly in
2895:Robust programming
2804:Linear programming
2797:Convex programming
2430:Subgradient method
2314:
2239:Conjugate gradient
2147:Nelder–Mead method
1978:CPLEX CP Optimizer
207:
87:Mathematics portal
34:content assessment
3037:Composite concave
3003:complementarities
2833:Conic programming
2785:
2784:
2768:
2767:
2708:
2707:
2704:
2703:
2667:
2666:
2628:
2627:
2524:
2523:
2520:
2519:
2516:
2515:
2387:
2386:
2383:
2382:
2303:
2302:
2299:
2298:
2277:
2276:
2046:
2045:
1952:
1951:
1948:
1947:
1826:
1825:
1522:
1521:
1518:
1517:
1484:
1483:
1374:
1373:
1370:
1369:
1291:
1290:
1071:
1070:
1067:
1066:
832:
831:
228:
227:
224:
223:
220:
219:
192:software articles
130:
129:
126:
125:
3554:
3346:Instance Formats
2989:Bellman equation
2889:random variables
2714:
2630:
2596:
2573:Branch and bound
2563:Greedy algorithm
2543:
2530:
2450:
2406:
2393:
2334:
2321:
2269:Truncated Newton
2184:Wolfe conditions
2167:
2120:
2107:
2080:
2073:
2066:
2057:
1987:Google CP Solver
1835:
1541:
1534:
1510:Xpress-Optimizer
1493:
1476:Xpress-Optimizer
1397:
1390:
1357:Xpress-Optimizer
1300:
1183:Xpress-Optimizer
1096:
1087:
1059:Xpress-Optimizer
998:Xpress-Optimizer
891:Xpress-Optimizer
841:
788:Xpress-Optimizer
645:Xpress-Optimizer
551:Xpress-Optimizer
439:
430:
267:
260:
253:
244:
194:
193:
190:
187:
184:
163:
156:
155:
150:
139:
132:
120:
119:
116:
113:
110:
89:
84:
83:
73:
66:
65:
55:
48:
25:
24:
23:
16:
3562:
3561:
3557:
3556:
3555:
3553:
3552:
3551:
3502:
3501:
3458:
3415:
3382:
3379:YALMIP: Solvers
3343:
3293:
3169:
3147:Complementarity
3106:
3025:
2979:Optimal control
2793:
2786:
2781:
2764:
2721:
2700:
2663:
2624:
2583:
2537:
2512:
2476:
2434:
2400:
2379:
2353:
2349:Penalty methods
2344:Barrier methods
2328:
2315:
2295:
2291:Newton's method
2273:
2225:
2188:
2156:
2137:Powell's method
2114:
2101:
2084:
2054:
2047:
2042:
2020:
1998:
1944:
1822:
1794:
1768:
1727:
1701:
1663:
1580:
1514:
1480:
1366:
1287:
1258:
1240:
1187:
1063:
1002:
895:
828:
792:
711:
680:
649:
555:
418:
320:
276:
271:
241:
233:
191:
188:
185:
182:
181:
145:
117:
114:
111:
108:
107:
85:
78:
12:
11:
5:
3560:
3558:
3550:
3549:
3544:
3539:
3534:
3529:
3524:
3519:
3514:
3504:
3503:
3500:
3499:
3498:
3497:
3492:
3484:
3479:
3474:
3469:
3464:
3457:
3454:
3453:
3452:
3449:
3446:
3443:
3440:
3437:
3434:
3431:
3428:
3425:
3422:
3419:
3414:
3409:
3408:
3407:
3404:
3401:
3398:
3395:
3392:
3389:
3386:
3381:
3372:
3371:
3370:
3364:
3359:
3356:
3353:
3350:
3347:
3342:
3337:
3336:
3335:
3334:
3333:
3330:
3327:
3321:
3318:
3315:
3312:
3309:
3306:
3303:
3300:
3297:
3292:
3287:
3286:
3285:
3282:
3279:
3278:
3277:
3274:
3271:
3268:
3265:
3262:
3256:
3255:
3254:
3253:
3252:
3243:
3242:
3241:
3240:
3239:
3233:
3232:
3231:
3222:
3221:
3220:
3219:
3218:
3215:
3209:
3206:
3203:
3200:
3197:
3194:
3191:
3188:
3185:
3182:
3179:
3176:
3168:
3159:
3158:
3157:
3154:
3151:
3148:
3145:
3142:
3141:
3140:
3137:
3134:
3131:
3128:
3125:
3122:
3119:
3113:
3110:
3105:
3100:
3099:
3098:
3095:
3092:
3089:
3088:Reverse convex
3086:
3085:Pseudo-boolean
3083:
3080:
3077:
3074:
3071:
3068:
3065:
3062:
3059:
3056:
3053:
3050:
3047:
3044:
3041:
3038:
3035:
3032:
3029:
3024:
3019:
3018:
3017:
3014:
3007:
3006:
2992:
2982:
2976:
2966:
2965:
2962:
2961:
2960:
2936:
2932:metaheuristics
2925:
2915:
2909:
2899:
2892:
2882:
2875:
2869:
2862:
2852:
2851:
2850:
2836:
2830:
2817:
2811:
2799:
2792:
2787:
2783:
2782:
2780:
2779:
2773:
2770:
2769:
2766:
2765:
2763:
2762:
2757:
2752:
2747:
2742:
2737:
2732:
2726:
2723:
2722:
2719:Metaheuristics
2717:
2710:
2709:
2706:
2705:
2702:
2701:
2699:
2698:
2693:
2691:Ford–Fulkerson
2688:
2683:
2677:
2675:
2669:
2668:
2665:
2664:
2662:
2661:
2659:Floyd–Warshall
2656:
2651:
2650:
2649:
2638:
2636:
2626:
2625:
2623:
2622:
2617:
2612:
2606:
2604:
2601:
2593:
2590:
2585:
2584:
2582:
2581:
2580:
2579:
2565:
2560:
2555:
2549:
2547:
2539:
2538:
2533:
2526:
2525:
2522:
2521:
2518:
2517:
2514:
2513:
2511:
2510:
2505:
2500:
2495:
2489:
2487:
2478:
2477:
2475:
2474:
2469:
2464:
2462:Affine scaling
2458:
2456:
2454:Interior point
2447:
2443:
2436:
2435:
2433:
2432:
2427:
2422:
2416:
2414:
2411:
2402:
2401:
2396:
2389:
2388:
2385:
2384:
2381:
2380:
2378:
2377:
2372:
2367:
2361:
2359:
2358:Differentiable
2355:
2354:
2352:
2351:
2346:
2340:
2338:
2330:
2329:
2324:
2317:
2316:
2306:
2304:
2301:
2300:
2297:
2296:
2294:
2293:
2287:
2285:
2279:
2278:
2275:
2274:
2272:
2271:
2266:
2261:
2256:
2251:
2246:
2241:
2235:
2233:
2227:
2226:
2224:
2223:
2218:
2213:
2204:
2198:
2196:
2190:
2189:
2187:
2186:
2181:
2175:
2173:
2164:
2158:
2157:
2155:
2154:
2149:
2144:
2139:
2134:
2128:
2126:
2116:
2115:
2110:
2103:
2102:
2085:
2083:
2082:
2075:
2068:
2060:
2053:
2048:
2044:
2043:
2041:
2040:
2033:
2025:
2022:
2021:
2019:
2018:
2015:
2009:
2007:
2000:
1999:
1997:
1996:
1993:
1988:
1985:
1980:
1975:
1970:
1967:
1963:
1961:
1954:
1953:
1950:
1949:
1946:
1945:
1943:
1942:
1937:
1932:
1927:
1922:
1917:
1912:
1907:
1904:
1899:
1894:
1889:
1884:
1879:
1874:
1869:
1864:
1859:
1854:
1849:
1843:
1841:
1832:
1828:
1827:
1824:
1823:
1821:
1820:
1815:
1810:
1804:
1802:
1796:
1795:
1793:
1792:
1787:
1782:
1776:
1774:
1770:
1769:
1767:
1766:
1761:
1756:
1751:
1746:
1741:
1735:
1733:
1732:LP/NLP-B&B
1729:
1728:
1726:
1725:
1720:
1715:
1709:
1707:
1703:
1702:
1700:
1699:
1694:
1689:
1684:
1679:
1673:
1671:
1665:
1664:
1662:
1661:
1656:
1651:
1646:
1641:
1636:
1631:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1590:
1588:
1582:
1581:
1579:
1578:
1573:
1568:
1563:
1558:
1555:
1549:
1547:
1538:
1531:
1524:
1523:
1520:
1519:
1516:
1515:
1513:
1512:
1507:
1501:
1499:
1490:
1486:
1485:
1482:
1481:
1479:
1478:
1473:
1468:
1463:
1458:
1453:
1448:
1443:
1438:
1433:
1428:
1423:
1418:
1413:
1408:
1402:
1400:
1394:
1387:
1376:
1375:
1372:
1371:
1368:
1367:
1365:
1364:
1359:
1354:
1349:
1344:
1339:
1334:
1329:
1324:
1319:
1314:
1308:
1306:
1297:
1293:
1292:
1289:
1288:
1286:
1285:
1280:
1275:
1269:
1267:
1260:
1259:
1257:
1256:
1250:
1248:
1242:
1241:
1239:
1238:
1233:
1228:
1223:
1218:
1213:
1208:
1203:
1197:
1195:
1189:
1188:
1186:
1185:
1180:
1175:
1170:
1165:
1160:
1155:
1150:
1145:
1140:
1135:
1130:
1125:
1120:
1115:
1110:
1104:
1102:
1093:
1084:
1073:
1072:
1069:
1068:
1065:
1064:
1062:
1061:
1056:
1051:
1046:
1041:
1038:
1033:
1028:
1023:
1018:
1012:
1010:
1004:
1003:
1001:
1000:
995:
990:
985:
982:
977:
972:
967:
962:
957:
954:
949:
944:
939:
934:
929:
924:
919:
914:
909:
905:
903:
897:
896:
894:
893:
888:
883:
878:
875:
870:
865:
860:
855:
849:
847:
838:
834:
833:
830:
829:
827:
826:
821:
816:
811:
806:
802:
800:
794:
793:
791:
790:
785:
782:
777:
772:
767:
762:
757:
752:
747:
742:
737:
732:
727:
721:
719:
713:
712:
710:
709:
704:
701:
696:
690:
688:
682:
681:
679:
678:
675:
670:
665:
659:
657:
651:
650:
648:
647:
642:
637:
634:
629:
624:
619:
614:
609:
604:
601:
596:
591:
586:
581:
576:
571:
565:
563:
557:
556:
554:
553:
548:
543:
538:
533:
528:
523:
518:
513:
508:
503:
498:
493:
488:
483:
478:
473:
468:
463:
458:
453:
447:
445:
436:
427:
420:
419:
417:
416:
411:
406:
401:
396:
393:
388:
383:
378:
373:
368:
363:
358:
355:
350:
347:
342:
337:
331:
329:
322:
321:
319:
318:
313:
308:
303:
298:
293:
288:
284:
282:
278:
277:
272:
270:
269:
262:
255:
247:
240:
234:
232:
229:
226:
225:
222:
221:
218:
217:
208:
198:
197:
195:
178:the discussion
164:
152:
151:
140:
128:
127:
124:
123:
121:
104:the discussion
91:
90:
74:
62:
61:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
3559:
3548:
3545:
3543:
3540:
3538:
3535:
3533:
3530:
3528:
3525:
3523:
3520:
3518:
3515:
3513:
3510:
3509:
3507:
3496:
3493:
3491:
3488:
3487:
3485:
3483:
3480:
3478:
3475:
3473:
3470:
3468:
3465:
3463:
3460:
3459:
3455:
3450:
3447:
3444:
3441:
3438:
3435:
3432:
3429:
3426:
3423:
3420:
3417:
3416:
3413:
3410:
3405:
3402:
3399:
3396:
3393:
3390:
3387:
3384:
3383:
3380:
3376:
3373:
3365:
3360:
3357:
3354:
3351:
3348:
3345:
3344:
3341:
3338:
3331:
3328:
3325:
3324:
3322:
3319:
3316:
3313:
3310:
3307:
3304:
3301:
3298:
3295:
3294:
3291:
3288:
3283:
3280:
3275:
3272:
3269:
3266:
3263:
3260:
3259:
3257:
3250:
3249:
3247:
3246:
3244:
3237:
3236:
3234:
3229:
3228:
3226:
3225:
3223:
3216:
3213:
3212:
3210:
3207:
3204:
3201:
3198:
3195:
3192:
3189:
3186:
3183:
3180:
3177:
3174:
3173:
3171:
3170:
3167:
3163:
3160:
3155:
3152:
3149:
3146:
3143:
3138:
3135:
3132:
3129:
3126:
3123:
3120:
3117:
3116:
3114:
3111:
3108:
3107:
3104:
3101:
3096:
3094:Semi-infinite
3093:
3091:Semi-definite
3090:
3087:
3084:
3081:
3078:
3076:Mixed-Integer
3075:
3072:
3069:
3066:
3063:
3060:
3057:
3054:
3051:
3048:
3045:
3042:
3039:
3036:
3033:
3030:
3027:
3026:
3023:
3020:
3015:
3012:
3011:
3010:
3004:
3000:
2996:
2993:
2990:
2986:
2983:
2980:
2977:
2974:
2971:
2970:
2969:
2963:
2958:
2955:
2954:
2952:
2948:
2944:
2940:
2937:
2933:
2929:
2926:
2923:
2919:
2916:
2913:
2910:
2907:
2903:
2900:
2896:
2893:
2890:
2886:
2883:
2879:
2876:
2873:
2870:
2866:
2863:
2860:
2856:
2853:
2848:
2844:
2840:
2837:
2834:
2831:
2828:
2825:
2821:
2818:
2815:
2812:
2809:
2805:
2802:
2801:
2798:
2795:
2794:
2791:
2788:
2778:
2775:
2774:
2771:
2761:
2758:
2756:
2753:
2751:
2748:
2746:
2743:
2741:
2738:
2736:
2735:Hill climbing
2733:
2731:
2728:
2727:
2724:
2720:
2715:
2711:
2697:
2694:
2692:
2689:
2687:
2684:
2682:
2679:
2678:
2676:
2674:
2673:Network flows
2670:
2660:
2657:
2655:
2652:
2648:
2645:
2644:
2643:
2640:
2639:
2637:
2635:
2634:Shortest path
2631:
2621:
2618:
2616:
2613:
2611:
2608:
2607:
2605:
2603:
2602:spanning tree
2597:
2594:
2592:
2586:
2578:
2574:
2571:
2570:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2550:
2548:
2544:
2540:
2536:
2535:Combinatorial
2531:
2527:
2509:
2506:
2504:
2501:
2499:
2496:
2494:
2491:
2490:
2488:
2486:
2483:
2479:
2473:
2470:
2468:
2465:
2463:
2460:
2459:
2457:
2455:
2451:
2448:
2446:
2441:
2437:
2431:
2428:
2426:
2423:
2421:
2418:
2417:
2415:
2413:
2407:
2403:
2399:
2394:
2390:
2376:
2373:
2371:
2368:
2366:
2363:
2362:
2360:
2356:
2350:
2347:
2345:
2342:
2341:
2339:
2335:
2331:
2327:
2322:
2318:
2310:
2292:
2289:
2288:
2286:
2284:
2280:
2270:
2267:
2265:
2262:
2260:
2257:
2255:
2252:
2250:
2247:
2245:
2242:
2240:
2237:
2236:
2234:
2232:
2231:Other methods
2228:
2222:
2219:
2217:
2214:
2212:
2208:
2205:
2203:
2200:
2199:
2197:
2195:
2191:
2185:
2182:
2180:
2177:
2176:
2174:
2172:
2168:
2165:
2163:
2159:
2153:
2150:
2148:
2145:
2143:
2140:
2138:
2135:
2133:
2130:
2129:
2127:
2125:
2121:
2117:
2113:
2108:
2104:
2100:
2096:
2092:
2088:
2081:
2076:
2074:
2069:
2067:
2062:
2061:
2058:
2052:
2049:
2039:
2038:
2034:
2032:
2031:
2027:
2026:
2023:
2016:
2014:
2011:
2010:
2008:
2005:
2004:Metaheuristic
2001:
1994:
1992:
1989:
1986:
1984:
1981:
1979:
1976:
1974:
1971:
1968:
1966:Artelys Kalis
1965:
1964:
1962:
1959:
1955:
1941:
1938:
1936:
1933:
1931:
1928:
1926:
1923:
1921:
1918:
1916:
1913:
1911:
1908:
1905:
1903:
1900:
1898:
1895:
1893:
1890:
1888:
1885:
1883:
1880:
1878:
1875:
1873:
1870:
1868:
1865:
1863:
1860:
1858:
1855:
1853:
1850:
1848:
1845:
1844:
1842:
1840:
1836:
1833:
1829:
1819:
1816:
1814:
1811:
1809:
1806:
1805:
1803:
1801:
1797:
1791:
1788:
1786:
1783:
1781:
1778:
1777:
1775:
1771:
1765:
1762:
1760:
1757:
1755:
1752:
1750:
1747:
1745:
1742:
1740:
1737:
1736:
1734:
1730:
1724:
1721:
1719:
1716:
1714:
1711:
1710:
1708:
1704:
1698:
1695:
1693:
1690:
1688:
1685:
1683:
1680:
1678:
1675:
1674:
1672:
1670:
1666:
1660:
1657:
1655:
1652:
1650:
1647:
1645:
1642:
1640:
1637:
1635:
1632:
1630:
1627:
1625:
1622:
1620:
1617:
1615:
1612:
1610:
1607:
1605:
1602:
1600:
1597:
1595:
1592:
1591:
1589:
1587:
1583:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1556:
1554:
1551:
1550:
1548:
1546:
1542:
1539:
1535:
1532:
1529:
1525:
1511:
1508:
1506:
1503:
1502:
1500:
1498:
1494:
1491:
1487:
1477:
1474:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1422:
1419:
1417:
1414:
1412:
1409:
1407:
1404:
1403:
1401:
1398:
1395:
1391:
1388:
1385:
1381:
1377:
1363:
1360:
1358:
1355:
1353:
1350:
1348:
1345:
1343:
1340:
1338:
1335:
1333:
1330:
1328:
1325:
1323:
1320:
1318:
1315:
1313:
1310:
1309:
1307:
1305:
1301:
1298:
1294:
1284:
1281:
1279:
1276:
1274:
1271:
1270:
1268:
1266:
1261:
1255:
1252:
1251:
1249:
1247:
1243:
1237:
1234:
1232:
1229:
1227:
1224:
1222:
1219:
1217:
1214:
1212:
1209:
1207:
1204:
1202:
1199:
1198:
1196:
1194:
1190:
1184:
1181:
1179:
1176:
1174:
1171:
1169:
1166:
1164:
1161:
1159:
1156:
1154:
1151:
1149:
1146:
1144:
1141:
1139:
1136:
1134:
1131:
1129:
1126:
1124:
1121:
1119:
1116:
1114:
1111:
1109:
1106:
1105:
1103:
1101:
1097:
1094:
1092:
1088:
1085:
1082:
1078:
1074:
1060:
1057:
1055:
1052:
1050:
1047:
1045:
1042:
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1022:
1019:
1017:
1014:
1013:
1011:
1009:
1005:
999:
996:
994:
991:
989:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
955:
953:
950:
948:
945:
943:
940:
938:
935:
933:
930:
928:
925:
923:
920:
918:
915:
913:
910:
907:
906:
904:
902:
898:
892:
889:
887:
884:
882:
879:
876:
874:
871:
869:
866:
864:
861:
859:
856:
854:
851:
850:
848:
846:
842:
839:
835:
825:
822:
820:
817:
815:
812:
810:
807:
804:
803:
801:
799:
795:
789:
786:
783:
781:
778:
776:
773:
771:
768:
766:
763:
761:
758:
756:
753:
751:
748:
746:
743:
741:
738:
736:
733:
731:
728:
726:
723:
722:
720:
718:
714:
708:
705:
702:
700:
697:
695:
692:
691:
689:
687:
683:
676:
674:
671:
669:
666:
664:
661:
660:
658:
656:
652:
646:
643:
641:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
602:
600:
597:
595:
592:
590:
587:
585:
582:
580:
577:
575:
572:
570:
567:
566:
564:
562:
558:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
472:
469:
467:
464:
462:
459:
457:
454:
452:
449:
448:
446:
444:
440:
437:
435:
431:
428:
425:
421:
415:
412:
410:
407:
405:
402:
400:
397:
394:
392:
389:
387:
384:
382:
379:
377:
374:
372:
369:
367:
364:
362:
359:
356:
354:
351:
348:
346:
343:
341:
338:
336:
333:
332:
330:
327:
323:
317:
314:
312:
309:
307:
304:
302:
299:
297:
294:
292:
289:
286:
285:
283:
279:
275:
268:
263:
261:
256:
254:
249:
248:
245:
239:
235:
230:
215:
214:
204:
200:
199:
196:
179:
175:
171:
170:
165:
162:
158:
157:
153:
149:
144:
141:
138:
134:
122:
105:
101:
97:
96:
88:
82:
77:
75:
72:
68:
67:
63:
60:
57:
54:
50:
45:
41:
35:
31:
27:
18:
17:
3008:
2967:
2942:
2868:programming.
2824:semidefinite
2807:
2740:Local search
2686:Edmonds–Karp
2642:Bellman–Ford
2412:minimization
2244:Gauss–Newton
2194:Quasi–Newton
2179:Trust region
2087:Optimization
2035:
2028:
1831:Formulations
1489:Formulations
1296:Formulations
837:Formulations
404:Xpress-Mosel
371:GNU MathProg
281:Data formats
257:
211:
167:
93:
40:WikiProjects
29:
3264:Game Theory
3049:Disjunctive
2922:dimensional
2843:posynomials
2760:Tabu search
2171:Convergence
2142:Line search
2017:LocalSolver
2013:OptaPlanner
1706:NLP-B&B
937:GLPK/GLPSOL
740:GLPK/GLPSOL
699:GLPK/GLPSOL
589:GLPK/GLPSOL
486:GLPK/GLPSOL
109:Mathematics
100:mathematics
59:Mathematics
3506:Categories
3079:Multilevel
3058:Fractional
3055:Factorable
3040:Continuous
2928:Heuristics
2591:algorithms
2099:heuristics
2091:Algorithms
1940:Xpress-SLP
1818:Xpress-SLP
1764:Xpress-SLP
1659:Xpress-SLP
1537:Algorithms
1393:Algorithms
1362:Xpress-SLP
1236:Xpress-SLP
1091:Algorithms
434:Algorithms
3130:NLP/MINLP
3097:Separable
3082:Nonlinear
3061:Geometric
2935:problems.
2847:monomials
2546:Paradigms
2445:quadratic
2162:Gradients
2124:Functions
1920:LINDO API
1609:LINDO API
1599:FilterSQP
1426:LINDO API
1347:LINDO API
1148:LINDO API
1036:LINDO API
952:LINDO API
873:LINDO API
755:LINDO API
677:Sulum NET
599:LINDO API
506:LINDO API
345:APMonitor
148:Computing
3124:SDP/SOCP
3067:Infinite
3046:Discrete
3034:Bilinear
3031:Biconvex
3028:Abstract
2906:discrete
2827:matrices
2777:Software
2654:Dijkstra
2485:exchange
2283:Hessians
2249:Gradient
1906:Minotaur
1902:MINLP_BB
1852:ANTIGONE
1847:AlphaECP
1808:AlphaECP
1718:MINLP_BB
1687:LANCELOT
1677:ALGENCAN
1557:ipfilter
1451:SCIP-SDP
1040:lp_solve
988:SYMPHONY
984:Sulum IP
956:lp_solve
877:lp_solve
824:SYMPHONY
784:Sulum IP
703:lp_solve
636:Sulum LP
603:lp_solve
481:GIPALS32
326:Modeling
183:Software
174:software
143:Software
30:template
3121:QP/MIQP
3118:LP/MILP
3070:Lattice
3064:Integer
3052:Dynamic
3009:Other:
2859:integer
2620:Kruskal
2610:BorĹŻvka
2600:Minimum
2337:General
2095:methods
2006:solvers
1960:solvers
1882:FilMINT
1872:Couenne
1749:FilMINT
1682:GALAHAD
1639:PATHNLP
1530:solvers
1386:solvers
1327:GloMIQO
1083:solvers
980:SOPT-IP
780:SOPT-IP
717:B&C
686:B&B
632:SOPT-IP
541:SOPT-IP
426:solvers
3323:Misc.
3073:Linear
3043:Convex
2482:Basis-
2440:Linear
2410:Convex
2254:Mirror
2211:L-BFGS
2097:, and
1983:Gecode
1897:MILANO
1892:MIDACO
1887:KNITRO
1877:DICOPT
1867:Bonmin
1813:Bonmin
1790:DICOPT
1785:Bonmin
1754:KNITRO
1744:Bonmin
1713:Bonmin
1697:PENNON
1649:SQPlab
1629:NLPQLP
1619:LRAMBO
1604:KNITRO
1594:CONOPT
1576:MILANO
1566:KNITRO
1471:SeDuMi
1441:PENSDP
1421:Gurobi
1342:KNITRO
1332:Gurobi
1322:FortMP
1283:Gurobi
1278:FortMP
1216:KNITRO
1143:KNITRO
1133:Gurobi
1128:FortMP
1044:SAS/OR
1031:Gurobi
1026:FortMP
970:SAS/OR
947:KNITRO
942:Gurobi
932:FortMP
908:ABACUS
868:Gurobi
863:FortMP
805:ABACUS
770:SAS/OR
750:KNITRO
745:Gurobi
735:FortMP
694:FortMP
673:SAS/OR
627:SoPlex
622:SAS/OR
594:Gurobi
584:FortMP
536:SAS/OR
501:KNITRO
491:Gurobi
476:FortMP
409:YALMIP
391:OptimJ
361:CVXOPT
36:scale.
2898:data.
2681:Dinic
2589:Graph
1995:OscaR
1991:JaCoP
1973:Comet
1969:Choco
1935:SNOPT
1915:OQNLP
1910:MISQP
1862:BARON
1739:APOPT
1692:MINOS
1654:WORHP
1644:SNOPT
1634:NPSOL
1624:MISQP
1561:IPOPT
1553:BPOPT
1505:MOSEK
1466:SDPT3
1461:SDPLR
1436:MOSEK
1406:CPLEX
1337:MOSEK
1317:CPLEX
1273:CPLEX
1254:MINOS
1231:QPOPT
1226:MINOS
1221:LSSOL
1201:APOPT
1173:QPSOL
1158:MOSEK
1138:IPOPT
1123:CPLEX
1113:BPOPT
1108:BPMPD
1021:CPLEX
965:MOSEK
960:MINTO
927:CPLEX
858:CPLEX
765:MOSEK
760:MINTO
730:CPLEX
668:MOSEK
663:CPLEX
617:QSopt
612:MOSEK
607:MINOS
579:CPLEX
569:BDMLP
516:MOSEK
496:HOPDM
461:CPLEX
451:BPMPD
414:ZIMPL
395:PICOS
376:LINDO
353:Coopr
335:AIMMS
328:tools
301:OptML
28:This
3377:and
3164:and
3001:or
2930:and
2908:one.
2647:SPFA
2615:Prim
2209:and
1930:SCIP
1759:SCIP
1614:LOQO
1571:LOQO
1456:SDPA
1446:SCIP
1431:LOQO
1416:DSDP
1411:CSDP
1380:SOCP
1352:SCIP
1206:BQPD
1168:OOQP
1163:OOPS
1153:LOQO
1049:SCIP
975:SCIP
881:SCIP
819:SCIP
775:SCIP
526:OOQP
521:OOPS
511:LOQO
471:DSDP
466:CSDP
399:PuLP
366:GAMS
349:CMPL
340:AMPL
316:xMPS
306:OSiL
3332:...
3284:...
3156:...
2953:).
2881:it.
2577:cut
2442:and
1925:SBB
1857:AOA
1839:INT
1800:CPM
1780:AOA
1723:SBB
1669:ALM
1586:ASM
1545:IPM
1528:NLP
1497:INT
1384:SDP
1312:CBC
1304:INT
1246:ALM
1211:CLP
1193:ASM
1118:CLP
1100:IPM
1081:QCP
1016:CBC
1008:SOS
922:GCG
917:CBC
912:BCP
901:INT
853:CBC
814:GCG
809:BCP
798:BCP
725:CBC
655:NSM
574:CLP
531:PCx
456:CLP
443:IPM
386:MPL
381:OPL
357:CVX
311:sol
291:MPS
3508::
2093:,
2089::
1958:CP
1773:OA
1382:/
1265:SM
1263:QP
1079:/
1077:QP
1054:XA
993:XA
886:XA
845:SC
707:XA
640:XA
561:SM
546:XA
424:LP
296:nl
287:LP
146::
3005:.
2991:.
2959:.
2943:f
2891:.
2808:f
2575:/
2079:e
2072:t
2065:v
266:e
259:t
252:v
216:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
