467:
955:
64:
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."
364:
235:
359:
1024:
1019:
1000:
373:
853:
79:
49:) of the model. The linearizations are linear programming problems, which can be solved efficiently. As the linearizations need not be bounded,
228:
160:
934:
396:
448:
309:
416:
183:
527:
221:
74:
61:
45:
Starting at some estimate of the optimal solution, the method is based on solving a sequence of first-order approximations (i.e.
804:
466:
912:
848:
816:
993:
193:
Palacios-Gomez, F.; Lasdon, L.; Enquist, M. (October 1982). "Nonlinear
Optimization by Successive Linear Programming".
897:
522:
84:
843:
799:
401:
692:
421:
582:
244:
767:
629:
986:
811:
710:
426:
304:
902:
887:
777:
655:
281:
248:
57:
35:
791:
757:
660:
602:
483:
289:
269:
838:
665:
577:
175:
213:
907:
772:
725:
715:
567:
555:
368:
351:
256:
39:
642:
611:
597:
587:
378:
294:
650:
328:
179:
156:
970:
730:
720:
624:
501:
406:
388:
341:
252:
202:
746:
152:
966:
734:
619:
506:
440:
411:
1013:
892:
876:
46:
830:
336:
50:
31:
917:
299:
962:
206:
319:
954:
639:
53:
or similar techniques are needed to ensure convergence in theory.
60:
since the 1970s. Since then, however, they have been superseded by
874:
690:
553:
481:
267:
217:
170:
Bazaraa, Mokhtar S.; Sherali, Hanif D.; Shetty, C.M. (1993).
465:
130:
974:
117:
829:
790:
756:
745:
703:
638:
610:
596:
566:
515:
494:
439:
387:
350:
327:
318:
280:
38:problems. It is related to, but distinct from,
172:Nonlinear Programming, Theory and Applications
994:
229:
104:
8:
147:Nocedal, Jorge; Wright, Stephen J. (2006).
1001:
987:
871:
787:
753:
700:
687:
607:
563:
550:
491:
478:
324:
277:
264:
236:
222:
214:
131:Palacios-Gomez, Lasdon & Enquist 1982
470:Optimization computes maxima and minima.
16:Approximation for nonlinear optimization
96:
80:Sequential linear-quadratic programming
666:Principal pivoting algorithm of Lemke
7:
1025:Algorithms and data structures stubs
951:
949:
34:technique for approximately solving
1020:Optimization algorithms and methods
973:. You can help Knowledge (XXG) by
310:Successive parabolic interpolation
151:(2nd ed.). 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:
1029:
1010:
1009:
1008:
1007:
967:data structures
946:
944:
939:
922:
879:
858:
821:
782:
759:
748:
741:
695:
670:
634:
601:
592:
569:
558:
537:
511:
507:Penalty methods
502:Barrier methods
486:
473:
453:
449:Newton's method
431:
383:
346:
314:
295:Powell's method
272:
259:
242:
192:
186:
169:
163:
153:Springer-Verlag
146:
143:
138:
137:
128:
124:
115:
111:
102:
98:
93:
71:
17:
12:
11:
5:
1038:
1036:
1028:
1027:
1022:
1012:
1011:
1006:
1005:
998:
991:
983:
980:
979:
958:
941:
940:
938:
937:
931:
928:
927:
924:
923:
921:
920:
915:
910:
905:
900:
895:
890:
884:
881:
880:
877:Metaheuristics
875:
868:
867:
864:
863:
860:
859:
857:
856:
851:
849:Ford–Fulkerson
846:
841:
835:
833:
827:
826:
823:
822:
820:
819:
817:Floyd–Warshall
814:
809:
808:
807:
796:
794:
784:
783:
781:
780:
775:
770:
764:
762:
751:
743:
742:
740:
739:
738:
737:
723:
718:
713:
707:
705:
697:
696:
691:
684:
683:
680:
679:
676:
675:
672:
671:
669:
668:
663:
658:
653:
647:
645:
636:
635:
633:
632:
627:
622:
620:Affine 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:
250:
246:
239:
234:
232:
227:
225:
220:
219:
216:
208:
204:
200:
196:
191:
187:
185:0-471-55793-5
181:
177:
173:
168:
164:
158:
154:
150:
145:
144:
140:
132:
126:
123:
119:
113:
110:
106:
100:
97:
90:
86:
83:
81:
78:
76:
73:
72:
68:
66:
63:
59:
54:
52:
51:trust regions
48:
43:
41:
37:
33:
29:
25:
21:
975:expanding it
960:
945:
898:Local search
844:Edmonds–Karp
800:Bellman–Ford
570:minimization
532:
402:Gauss–Newton
352:Quasi–Newton
337:Trust region
245:Optimization
198:
194:
171:
148:
125:
112:
99:
55:
44:
32:optimization
27:
23:
19:
18:
918:Tabu search
329:Convergence
300:Line search
1014:Categories
963:algorithms
749:algorithms
257:heuristics
249:Algorithms
91:References
704:Paradigms
603:quadratic
320:Gradients
282:Functions
30:, is an
935:Software
812:Dijkstra
643:exchange
441:Hessians
407:Gradient
69:See also
778:Kruskal
768:BorĹŻvka
758:Minimum
495:General
253:methods
141:Sources
640:Basis-
598:Linear
568:Convex
412:Mirror
369:L-BFGS
255:, and
182:
159:
961:This
839:Dinic
747:Graph
971:stub
805:SPFA
773:Prim
367:and
180:ISBN
157:ISBN
965:or
735:cut
600:and
203:doi
24:SLP
1016::
251:,
247::
199:28
197:.
178:.
155:.
42:.
1002:e
995:t
988:v
977:.
733:/
237:e
230:t
223:v
209:.
205::
188:.
165:.
133:)
129:(
116:(
103:(
22:(
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.