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|
|
Solution of a Large-Scale Traveling-Salesman Problem |
|
|
7 | (22) |
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|
|
|
The Hungarian Method for the Assignment Problem |
|
|
29 | (20) |
|
|
Integral Boundary Points of Convex Polyhedra |
|
|
49 | (28) |
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|
|
Outline of an Algorithm for Integer Solutions to Linear Programs and An Algorithm for the Mixed Integer Problem |
|
|
77 | (28) |
|
|
An Automatic Method for Solving Discrete Programming Problems |
|
|
105 | (28) |
|
|
|
Integer Programming: Methods, Uses, Computation |
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|
133 | (66) |
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|
|
199 | (20) |
|
|
Reducibility Among Combinatorial Problems |
|
|
219 | (24) |
|
|
Lagrangian Relaxation for Integer Programming |
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|
243 | (40) |
|
|
|
283 | (60) |
|
|
Part II From the Beginnings to the State-of-the-Art |
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|
|
Polyhedral Approaches to Mixed Integer Linear Programming |
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|
343 | (44) |
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|
|
|
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343 | (5) |
|
Mixed integer linear programming |
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|
343 | (1) |
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|
344 | (1) |
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|
345 | (3) |
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Polyhedra and the fundamental theorem of integer programming |
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|
348 | (11) |
|
Farkas' lemma and linear programming duality |
|
|
349 | (3) |
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|
352 | (1) |
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The theorem of Minkowski-Weyl |
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|
353 | (2) |
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|
355 | (1) |
|
The fundamental theorem for MILP |
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|
356 | (1) |
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|
357 | (1) |
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|
357 | (2) |
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359 | (3) |
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362 | (4) |
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One-side splits, Chvatal inequalities |
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|
365 | (1) |
|
Gomory's mixed-integer inequalities |
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|
366 | (3) |
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Equivalence of split closure and Gomory mixed integer closure |
|
|
368 | (1) |
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Polyhedrality of closures |
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369 | (4) |
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The Chvatal closure of a pure integer set |
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|
370 | (1) |
|
The split closure of a mixed integer set |
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370 | (3) |
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373 | (7) |
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374 | (2) |
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Strengthened lift-and-project cuts |
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|
376 | (1) |
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Improving mixed integer Gomory cuts by lift-and-project |
|
|
377 | (1) |
|
Sequential convexification |
|
|
378 | (2) |
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|
380 | (7) |
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|
380 | (2) |
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|
382 | (2) |
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|
384 | (3) |
|
Fifty-Plus Years of Combinatorial Integer Programming |
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|
387 | (44) |
|
|
Combinatorial integer programming |
|
|
387 | (2) |
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|
389 | (8) |
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Proving theorems with linear-programming duality |
|
|
397 | (2) |
|
Cutting-plane computation |
|
|
399 | (5) |
|
Jack Edmonds, polynomial-time algorithms, and polyhedral combinatorics |
|
|
404 | (6) |
|
Progress in the solution of the TSP |
|
|
410 | (5) |
|
Widening the field of application in the 1980s |
|
|
415 | (3) |
|
Optimization = Separation |
|
|
418 | (2) |
|
|
420 | (11) |
|
|
425 | (6) |
|
Reformulation and Decomposition of Integer Programs |
|
|
431 | (74) |
|
|
|
|
431 | (2) |
|
Polyhedra, reformulation and decomposition |
|
|
433 | (8) |
|
|
433 | (1) |
|
Polyhedra and reformulation |
|
|
434 | (6) |
|
|
440 | (1) |
|
Price or constraint decomposition |
|
|
441 | (23) |
|
Lagrangean relaxation and the Lagrangean dual |
|
|
443 | (2) |
|
Dantzig-Wolfe reformulations |
|
|
445 | (3) |
|
Solving the Dantzig-Wolfe relaxation by column generation |
|
|
448 | (3) |
|
Alternative methods for solving the Lagrangean dual |
|
|
451 | (5) |
|
Optimal integer solutions: branch-and-price |
|
|
456 | (8) |
|
|
464 | (1) |
|
Resource or variable decomposition |
|
|
464 | (7) |
|
|
465 | (3) |
|
Benders with integer subproblems |
|
|
468 | (2) |
|
|
470 | (1) |
|
|
471 | (1) |
|
Extended formulations: problem specific approaches |
|
|
471 | (19) |
|
Using compact extended formulations |
|
|
472 | (1) |
|
Variable splitting I: multi-commodity extended formulations |
|
|
473 | (4) |
|
|
477 | (3) |
|
Reformulations based on dynamic programming |
|
|
480 | (3) |
|
|
483 | (2) |
|
From polyhedra and separation to extended formulations |
|
|
485 | (2) |
|
Miscellaneous reformulations |
|
|
487 | (2) |
|
Existence of polynomial size extended formulations |
|
|
489 | (1) |
|
Hybrid algorithms and stronger dual bounds |
|
|
490 | (3) |
|
Lagrangean decomposition or price-and-price |
|
|
490 | (1) |
|
|
491 | (2) |
|
|
493 | (12) |
|
|
494 | (1) |
|
Dantzig-Wolfe and price decomposition |
|
|
494 | (2) |
|
|
496 | (1) |
|
|
496 | (2) |
|
Hybrid algorithms and stronger dual bounds |
|
|
498 | (1) |
|
|
498 | (7) |
|
|
|
Integer Programming and Algorithmic Geometry of Numbers |
|
|
505 | (56) |
|
|
Lattices, integer programming and the geometry of numbers |
|
|
505 | (2) |
|
Informal introduction to basis reduction |
|
|
507 | (2) |
|
|
509 | (6) |
|
|
515 | (3) |
|
|
518 | (7) |
|
Kannan's shortest vector algorithm |
|
|
525 | (4) |
|
A randomized simply exponential algorithm for shortest vector |
|
|
529 | (6) |
|
Integer programming in fixed dimension |
|
|
535 | (7) |
|
The integer linear optimization problem |
|
|
542 | (3) |
|
Diophantine approximation and strongly polynomial algorithms |
|
|
545 | (5) |
|
Parametric integer programming |
|
|
550 | (11) |
|
|
556 | (5) |
|
Nonlinear Integer Programming |
|
|
561 | (58) |
|
|
|
|
|
|
562 | (2) |
|
Convex integer maximization |
|
|
564 | (9) |
|
|
564 | (1) |
|
Boundary cases of complexity |
|
|
565 | (3) |
|
Reduction to linear integer programming |
|
|
568 | (5) |
|
Convex integer minimization |
|
|
573 | (13) |
|
|
573 | (4) |
|
Boundary cases of complexity |
|
|
577 | (3) |
|
|
580 | (6) |
|
|
586 | (18) |
|
Fixed dimension and linear constraints: An FPTAS |
|
|
587 | (10) |
|
Semi-algebraic sets and SOS programming |
|
|
597 | (4) |
|
|
601 | (3) |
|
|
604 | (7) |
|
|
605 | (2) |
|
Boundary cases of complexity |
|
|
607 | (4) |
|
|
611 | (8) |
|
|
612 | (7) |
|
Mixed Integer Programming Computation |
|
|
619 | (28) |
|
|
|
619 | (2) |
|
|
621 | (11) |
|
A performance perspective |
|
|
624 | (7) |
|
A modeling/application perspective |
|
|
631 | (1) |
|
|
632 | (9) |
|
A performance perspective |
|
|
634 | (5) |
|
|
639 | (2) |
|
|
641 | (6) |
|
|
642 | (5) |
|
Symmetry in Integer Linear Programming |
|
|
647 | (40) |
|
|
|
647 | (2) |
|
|
649 | (2) |
|
|
651 | (2) |
|
|
653 | (1) |
|
|
653 | (3) |
|
Symmetric polyhedra and related topics |
|
|
656 | (2) |
|
|
658 | (5) |
|
Dantzig-Wolfe decomposition |
|
|
659 | (1) |
|
|
660 | (2) |
|
Asymmetric representatives |
|
|
662 | (1) |
|
symmetry breaking inequalities |
|
|
663 | (5) |
|
Dynamic symmetry breaking inequalities |
|
|
664 | (1) |
|
Static symmetry breaking inequalities |
|
|
664 | (4) |
|
Pruning the enumeration tree |
|
|
668 | (6) |
|
Pruning with a fixed order on the variables |
|
|
670 | (3) |
|
Pruning without a fixed order of the variables |
|
|
673 | (1) |
|
Group representation and operations |
|
|
674 | (4) |
|
Enumerating all non-isomorphic solutions |
|
|
678 | (1) |
|
Furthering the reach of isomorphism pruning |
|
|
679 | (1) |
|
|
679 | (2) |
|
Exploiting additional symmetries |
|
|
681 | (6) |
|
|
681 | (6) |
|
Semidefinite Relaxations for Integer Programming |
|
|
687 | (40) |
|
|
|
687 | (3) |
|
Basics on semidefinite optimization |
|
|
690 | (2) |
|
Modeling with semidefinite programs |
|
|
692 | (13) |
|
Quadratic 0/1 optimization |
|
|
692 | (1) |
|
Max-Cut and graph bisection |
|
|
693 | (1) |
|
Stable sets, cliques and the Lovasz theta function |
|
|
694 | (2) |
|
|
696 | (2) |
|
|
698 | (2) |
|
|
700 | (2) |
|
SDP, eigenvalues and the Hoffman-Wielandt inequality |
|
|
702 | (3) |
|
The theoretical power of SDP |
|
|
705 | (6) |
|
Hyperplane rounding for Max-Cut |
|
|
705 | (3) |
|
|
708 | (3) |
|
|
711 | (10) |
|
Interior point algorithms |
|
|
711 | (4) |
|
Partial Lagrangian and the bundle method |
|
|
715 | (3) |
|
The spectral bundle method |
|
|
718 | (3) |
|
|
721 | (6) |
|
Copositive and completely positive matrices |
|
|
721 | (1) |
|
|
722 | (1) |
|
|
723 | (4) |
|
The Group-Theoretic Approach in Mixed Integer Programming |
|
|
727 | |
|
|
|
|
727 | |
|
|
730 | |
|
Linear programming relaxations |
|
|
730 | |
|
|
731 | |
|
Gomory's corner relaxation |
|
|
737 | |
|
Group relaxations: optimal solutions and structure |
|
|
739 | |
|
Optimizing linear functions over the corner relaxation |
|
|
739 | |
|
Using corner relaxations to solve MIPs |
|
|
744 | |
|
Extended group relaxations |
|
|
749 | |
|
Master group relaxations: definitions and inequalities |
|
|
754 | |
|
|
754 | |
|
Master group relaxations of mixed integer programs |
|
|
756 | |
|
A hierarchy of inequalities for master group problems |
|
|
759 | |
|
|
766 | |
|
Extreme inequalities of finite master group problems |
|
|
766 | |
|
Extreme inequalities for infinite group problems |
|
|
769 | |
|
A compendium of known extreme inequalities for finite and infinite group problems |
|
|
784 | |
|
On the strength of group cuts and the group approach |
|
|
785 | |
|
Absolute strength of group relaxation |
|
|
785 | |
|
Relative strength of different families of group cuts |
|
|
788 | |
|
Summary on strength of group cuts |
|
|
795 | |
|
Conclusion and perspectives |
|
|
795 | |
|
|
797 | |
|
Part IV DVD-Video/DVD-ROM |
|
|