A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

Júdice, Joaquim J.; Sherali, Hanif D.; Ribeiro, Isabel M.; Faustino, Ana M.

doi:10.1007/s10898-006-9001-8

Cited by 29 publications

(15 citation statements)

References 23 publications

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“…Write (19) as Now remember Example 2.7: V may have several representations. Any such representation ρ supports a set G ρ and we will see that the polar of G ρ is again V itself; G ρ is a pre-image of V for the polarity mapping.…”

Section: Largest and Smallest Representationsmentioning

confidence: 99%

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Cut-Generating Functions and S-Free Sets

et al. 2015

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We consider the separation problem for sets X that are pre-images of a given set S by a linear mapping. Classical examples occur in integer programming, as well as in other optimization problems such as complementarity. One would like to generate valid inequalities that cut off some point not lying in X, without reference to the linear mapping. To this aim, we introduce a concept: cut-generating functions (cgf) and we develop a formal theory for them, largely based on convex analysis. They are intimately related to S-free sets and we study this relation, disclosing several definitions for minimal cgf's and maximal S-free sets. Our work unifies and puts in perspective a number of existing works on S-free sets; in particular, we show how cgf's recover the celebrated Gomory cuts.

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Section: Largest and Smallest Representationsmentioning

confidence: 99%

“…The next result introduces the polar cone (V ∞ ) • . When G is a cone, positive homogeneity can be used to replace the righthand side "1" in (19) by any positive number, or even by "0": in particular,…”

Section: Smallest Representationmentioning

confidence: 99%

Cut-Generating Functions and S-Free Sets

et al. 2015

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“…, k, and give rise to simple disjunctions x i = 0 ∨ y j = 0. Júdice et al [33] studied an MPEC where the only nonlinear constraints are the complementarity constraints. Relaxing the latter yields an LP.…”

Section: Mathematical Programs With Equilibrium Constraints (Mpec)mentioning

confidence: 99%

Disjunctive Inequalities: Applications And Extensions

Belotti

Liberti

Lodi

et al. 2011

Wiley Encyclopedia of Operations Research and Management Science

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We survey some applications and extensions of disjunctive programming with special emphasis on recent developments. Specifically, after recalling the basic ingredients of disjunctive inequalities we report on recent results in the context of mixed integer linear programming. We then consider the application of disjunctive constraints both as modeling tool and cutting planes in mixed integer nonlinear programming. Finally, we discuss the application of disjunctions as branching conditions in enumerative algorithms, as opposed to the cutting approach.

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“…There are some algorithms to perform this task when the objective function is convex [1,9,10,13]. However, the function of the MPEC (4) is not convex, which precludes the use of such techniques.…”

Section: Theorem 2 If the Eicp Has A Solution Then There Existsmentioning

confidence: 99%

The eigenvalue complementarity problem

2007

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In this paper an eigenvalue complementarity problem (EiCP) is studied, which finds its origins in the solution of a contact problem in mechanics. The EiCP is shown to be equivalent to a Nonlinear Complementarity Problem, a Mathematical Programming Problem with Complementarity Constraints and a Global Optimization Problem. A finite Reformulation-Linearization Technique (RLT)-based tree search algorithm is introduced for processing the EiCP via the lattermost of these formulations. Computational experience is included to highlight the efficacy of the above formulations and corresponding techniques for the solution of the EiCP.

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A Complementarity-based Partitioning and Disjunctive Cut Algorithm for Mathematical Programming Problems with Equilibrium Constraints

Cited by 29 publications

References 23 publications

Cut-Generating Functions and S-Free Sets

Cut-Generating Functions and S-Free Sets

Disjunctive Inequalities: Applications And Extensions

The eigenvalue complementarity problem

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