Knowledge (XXG)

Successive linear programming

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methods. While solving a QP subproblem takes more time than solving an LP one, the overall decrease in the number of iterations, due to improved convergence, results in significantly lower running times and fewer function evaluations."
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Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order approximations (i.e.
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Palacios-Gomez, F.; Lasdon, L.; Enquist, M. (October 1982). "Nonlinear Optimization by Successive Linear Programming".
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or similar techniques are needed to ensure convergence in theory.
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since the 1970s. Since then, however, they have been superseded by
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Bazaraa, Mokhtar S.; Sherali, Hanif D.; Shetty, C.M. (1993).
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Berlin, New York: 118:Bazaraa, Sherali & Shetty 1993 14: 630:Projective algorithm of Karmarkar 953: 625:Ellipsoid algorithm of Khachiyan 528:Sequential quadratic programming 365:Broyden–Fletcher–Goldfarb–Shanno 75:Sequential quadratic programming 62:sequential quadratic programming 56:SLP has been used widely in the 583:Reduced gradient (Frank–Wolfe) 1: 913:Spiral optimization algorithm 533:Successive linear programming 28:Sequential Linear Programming 20:Successive Linear Programming 651:Simplex algorithm of Dantzig 523:Augmented Lagrangian methods 85:Augmented Lagrangian method 1041: 948: 930: 883: 870: 854:Push–relabel maximum flow 699: 686: 656:Revised simplex algorithm 562: 549: 490: 477: 463: 276: 263: 105:Nocedal & Wright 2006 379:Symmetric rank-one (SR1) 360:Berndt–Hall–Hall–Hausman 903:Parallel metaheuristics 711:Approximation algorithm 422:Powell's dog leg method 374:Davidon–Fletcher–Powell 270:Unconstrained nonlinear 207:10.1287/mnsc.28.10.1106 969:-related article is a 888:Evolutionary algorithm 471: 149:Numerical Optimization 58:petrochemical industry 36:nonlinear optimization 661:Criss-cross algorithm 484:Constrained nonlinear 469: 290:Golden-section search 176:John Wiley & Sons 578:Cutting-plane method 40:quasi-Newton methods 908:Simulated annealing 726:Integer programming 716:Dynamic programming 556:Convex optimization 417:Levenberg–Marquardt 588:Subgradient method 472: 397:Conjugate gradient 305:Nelder–Mead method 195:Management Science 982: 981: 943: 942: 926: 925: 866: 865: 862: 861: 825: 824: 786: 785: 682: 681: 678: 677: 674: 673: 545: 544: 541: 540: 461: 460: 457: 456: 435: 434: 201:(10): 1106–1120. 162:978-0-387-30303-1 26:), also known as 1032: 1003: 996: 989: 957: 950: 872: 788: 754: 731:Branch and bound 721:Greedy algorithm 701: 688: 608: 564: 551: 492: 479: 427:Truncated Newton 342:Wolfe conditions 325: 278: 265: 238: 231: 224: 215: 210: 189: 174:(2nd ed.). 166: 134: 127: 121: 114: 108: 101: 1040: 1039: 1035: 1034: 1033: 1031: 1030: 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scaling 616: 614: 612:Interior point 605: 594: 593: 591: 590: 585: 580: 574: 572: 560: 559: 554: 547: 546: 543: 542: 539: 538: 536: 535: 530: 525: 519: 517: 516:Differentiable 513: 512: 510: 509: 504: 498: 496: 488: 487: 482: 475: 474: 464: 462: 459: 458: 455: 454: 452: 451: 445: 443: 437: 436: 433: 432: 430: 429: 424: 419: 414: 409: 404: 399: 393: 391: 385: 384: 382: 381: 376: 371: 362: 356: 354: 348: 347: 345: 344: 339: 333: 331: 322: 316: 315: 313: 312: 307: 302: 297: 292: 286: 284: 274: 273: 268: 261: 260: 243: 241: 240: 233: 226: 218: 212: 211: 190: 184: 167: 161: 142: 139: 136: 135: 122: 120:, p. 432) 109: 107:, p. 551) 95: 94: 92: 89: 88: 87: 82: 77: 70: 67: 47:linearizations 15: 13: 10: 9: 6: 4: 3: 2: 1037: 1026: 1023: 1021: 1018: 1017: 1015: 1004: 999: 997: 992: 990: 985: 984: 978: 976: 972: 968: 964: 959: 956: 952: 947: 936: 933: 932: 929: 919: 916: 914: 911: 909: 906: 904: 901: 899: 896: 894: 893:Hill climbing 891: 889: 886: 885: 882: 878: 873: 869: 855: 852: 850: 847: 845: 842: 840: 837: 836: 834: 832: 831:Network flows 828: 818: 815: 813: 810: 806: 803: 802: 801: 798: 797: 795: 793: 792:Shortest path 789: 779: 776: 774: 771: 769: 766: 765: 763: 761: 760:spanning tree 755: 752: 750: 744: 736: 732: 729: 728: 727: 724: 722: 719: 717: 714: 712: 709: 708: 706: 702: 698: 694: 693:Combinatorial 689: 685: 667: 664: 662: 659: 657: 654: 652: 649: 648: 646: 644: 641: 637: 631: 628: 626: 623: 621: 618: 617: 615: 613: 609: 606: 604: 599: 595: 589: 586: 584: 581: 579: 576: 575: 573: 571: 565: 561: 557: 552: 548: 534: 531: 529: 526: 524: 521: 520: 518: 514: 508: 505: 503: 500: 499: 497: 493: 489: 485: 480: 476: 468: 450: 447: 446: 444: 442: 438: 428: 425: 423: 420: 418: 415: 413: 410: 408: 405: 403: 400: 398: 395: 394: 392: 390: 389:Other methods 386: 380: 377: 375: 372: 370: 366: 363: 361: 358: 357: 355: 353: 349: 343: 340: 338: 335: 334: 332: 330: 326: 323: 321: 317: 311: 308: 306: 303: 301: 298: 296: 293: 291: 288: 287: 285: 283: 279: 275: 271: 266: 262: 258: 254: 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Index

optimization
nonlinear optimization
quasi-Newton methods
linearizations
trust regions
petrochemical industry
sequential quadratic programming
Sequential quadratic programming
Sequential linear-quadratic programming
Augmented Lagrangian method
Nocedal & Wright 2006
Bazaraa, Sherali & Shetty 1993
Palacios-Gomez, Lasdon & Enquist 1982
Springer-Verlag
ISBN
978-0-387-30303-1
John Wiley & Sons
ISBN
0-471-55793-5
doi
10.1287/mnsc.28.10.1106
v
t
e
Optimization
Algorithms
methods
heuristics
Unconstrained nonlinear
Functions

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