A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints

Ribeiro, Ademir A.; Sachine, Mael; Krulikovski, Evelin H. M.

doi:10.1007/s10957-022-02007-0

Cited by 7 publications

(2 citation statements)

References 19 publications

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“…In fact, it is known that, for certain classes of optimization problems like cardinality-constrained problems, the standard AKKT-conditions hold at every feasible point, cf. [31]. The following example shows that this unfortunate situation does not hold in our setting with AS-stationarity.…”

Section: Approximate S-stationaritymentioning

confidence: 82%

Inexact penalty decomposition methods for optimization problems with geometric constraints

Kanzow

Lapucci

2023

Comput Optim Appl

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This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints are nonconvex and complicated, like cardinality constraints, disjunctive programs, or matrix problems involving rank constraints. By a variable duplication and decomposition strategy, the method presented here explicitly handles these difficult constraints, thus generating iterates which are feasible with respect to them, while the remaining (standard and supposingly simple) constraints are tackled by sequential penalization. Inexact optimization steps are proven sufficient for the resulting algorithm to work, so that it is employable even with difficult objective functions. The current work is therefore a significant generalization of existing papers on penalty decomposition methods. On the other hand, it is related to some recent publications which use an augmented Lagrangian idea to solve optimization problems with geometric constraints. Compared to these methods, the decomposition idea is shown to be numerically superior since it allows much more freedom in the choice of the subproblem solver, and since the number of certain (possibly expensive) projection steps is significantly less. Extensive numerical results on several highly complicated classes of optimization problems in vector and matrix spaces indicate that the current method is indeed very efficient to solve these problems.

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Section: Approximate S-stationaritymentioning

confidence: 82%

Inexact penalty decomposition methods for optimization problems with geometric constraints

Kanzow

Lapucci

2023

Comput Optim Appl

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“…This idea has been deeply exploited to provide constraints qualification, algorithms and first-order optimality conditions (see, e.g., [19,8,24,28,27,31]). But this analysis has been systematically limited to single level optimization problems.…”

Section: Introductionmentioning

confidence: 99%

A Short State of the Art on Multi-Leader-Follower Games

Aussel

Svensson

2020

Springer Optimization and Its Applications

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This work explores bilevel problems in the context of cardinality constraints. More specifically Single-Leader-Multi-Follower games (SLMFG) involving cardinality constraints are considered in two different configurations: one with the cardinality constraint at the leader's level and a mixed structure in which the cardinality constraint is split between leader and followers problem. We prove existence results in both cases and provided equivalent reformulations allowing the numerical treatment of these complex problems. The obtained results are illustrated thanks to an application to a facility location problem.

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A strong sequential optimality condition for cardinality-constrained optimization problems

Xue

Pang

2022

Numer Algor

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A Comparative Study of Sequential Optimality Conditions for Mathematical Programs with Cardinality Constraints

Cited by 7 publications

References 19 publications

Inexact penalty decomposition methods for optimization problems with geometric constraints

Inexact penalty decomposition methods for optimization problems with geometric constraints

A Short State of the Art on Multi-Leader-Follower Games

A strong sequential optimality condition for cardinality-constrained optimization problems

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