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95:) or constraint programs, any constraint program can be formulated as an integer program and vice versa, and constraint and integer programs can often be given a combinatorial interpretation.
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These branches are all closely intertwined however, since many combinatorial optimization problems can be modeled as integer programs (e.g.
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130:, Cambridge Texts in Applied Mathematics, vol. 36, Cambridge University Press, p. 1,
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Hammer, P. L.; Johnson, E. L.; Korte, B. H. (2000), "Conclusive remarks",
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155:, Annals of Discrete Mathematics, vol. 5, Elsevier, pp. 427–453
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used in a discrete optimization problem are restricted to be
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Three notable branches of discrete optimization are:
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127:A First Course in Combinatorial Optimization
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186:
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432:
420:Optimization computes maxima and minima.
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640:
616:Principal pivoting algorithm of Lemke
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16:Branch of mathematical optimization
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260:Successive parabolic interpolation
14:
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641:
580:Projective algorithm of Karmarkar
46:—that is, to assume only a
575:Ellipsoid algorithm of Khachiyan
478:Sequential quadratic programming
315:Broyden–Fletcher–Goldfarb–Shanno
533:Reduced gradient (Frank–Wolfe)
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117:
69:, which refers to problems on
1:
863:Spiral optimization algorithm
483:Successive linear programming
110:
77:and other discrete structures
601:Simplex algorithm of Dantzig
473:Augmented Lagrangian methods
7:
98:
57:
50:set of values, such as the
10:
922:
67:combinatorial optimization
906:Mathematical optimization
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833:
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804:Push–relabel maximum flow
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606:Revised simplex algorithm
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329:Symmetric rank-one (SR1)
310:Berndt–Hall–Hall–Hausman
153:Discrete Optimization II
853:Parallel metaheuristics
661:Approximation algorithm
372:Powell's dog leg method
324:Davidon–Fletcher–Powell
220:Unconstrained nonlinear
36:continuous optimization
838:Evolutionary algorithm
421:
86:constraint programming
611:Criss-cross algorithm
434:Constrained nonlinear
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240:Golden-section search
38:, some or all of the
20:Discrete optimization
528:Cutting-plane method
105:Diophantine equation
858:Simulated annealing
676:Integer programming
666:Dynamic programming
506:Convex optimization
367:Levenberg–Marquardt
81:integer programming
28:applied mathematics
538:Subgradient method
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347:Conjugate gradient
255:Nelder–Mead method
44:discrete variables
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124:Lee, Jon (2004),
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681:Branch and bound
671:Greedy algorithm
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34:. As opposed to
32:computer science
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457:Penalty methods
452:Barrier methods
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22:is a branch of
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827:Metaheuristics
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781:Network flows
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742:Shortest path
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710:spanning tree
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643:Combinatorial
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339:Other methods
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93:shortest path
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848:Local search
794:Edmonds–Karp
750:Bellman–Ford
520:minimization
352:Gauss–Newton
302:Quasi–Newton
287:Trust region
195:Optimization
152:
146:
126:
119:
90:
61:
24:optimization
19:
18:
868:Tabu search
279:Convergence
250:Line search
699:algorithms
207:heuristics
199:Algorithms
111:References
654:Paradigms
553:quadratic
270:Gradients
232:Functions
40:variables
900:Category
885:Software
762:Dijkstra
593:exchange
391:Hessians
357:Gradient
99:See also
75:matroids
58:Branches
52:integers
48:discrete
728:Kruskal
718:BorĹŻvka
708:Minimum
445:General
203:methods
590:Basis-
548:Linear
518:Convex
362:Mirror
319:L-BFGS
205:, and
134:
71:graphs
789:Dinic
697:Graph
755:SPFA
723:Prim
317:and
132:ISBN
30:and
685:cut
550:and
26:in
902::
201:,
197::
73:,
54:.
683:/
187:e
180:t
173:v
157:.
141:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.