Second order variational analysis of disjunctive constraint sets and its applications to optimization problems

Thinh, Vo Duc; Chương, Thái Doãn; Anh, Nguyen Le Hoang

doi:10.1007/s11590-020-01681-1

Cited by 3 publications

(1 citation statement)

References 34 publications

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“…So far there are many MPDC variants of constraint qualifications and optimality conditions have been introduced and studied in the literature (see e.g. [7,8,14,15,29,30,38]); see Liang and Ye [27,Section 3] for a survey on most of these conditions.…”

Section: Introductionmentioning

confidence: 99%

Relaxed constant positive linear dependence constraint qualification for disjunctive programs

Xu¹,

Ye²

2022

Preprint

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The disjunctive program is a class of optimization problems in which the constraint involves a disjunctive set which is the union of finitely many polyhedral convex sets. In this paper, we introduce a notion of the relaxed constant positive linear dependence constraint qualification (RCPLD) for the disjunctive program. Our notion is weaker than the one we introduced for a nonsmooth system which includes an abstract set constraint recently (J. Glob. Optim. 2020) and is still a constraint qualification for a Mordukhovich stationarity condition for the disjunctive program. To obtain the error bound property for the disjunctive program, we introduce the piecewise RCPLD under which the error bound property holds if all inequality constraint functions are subdifferentially regular and the rest of the constraint functions are smooth. We then specialize our results to the ortho-disjunctive program, which includes the mathematical program with equilibrium constraints (MPEC), the mathematical program with vanishing constraints (MPVC) and the mathematical program with switching constraints (MPSC) as special cases. For MPEC, we recover MPEC-RCPLD, an MPEC variant of RCPLD and propose the MPEC piecewise RCPLD to obtain the error bound property. For MPVC, we introduce MPVC-RCPLD as a constraint qualification and the piecewise RCPLD as a sufficient condition for the error bound property. For MPSC, we show that both RCPLD and the piecewise RCPLD coincide and hence it is not only a constraint qualification, but also a sufficient condition for the error bound property.

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Section: Introductionmentioning

confidence: 99%

Relaxed constant positive linear dependence constraint qualification for disjunctive programs

Xu¹,

Ye²

2022

Preprint

View full text Add to dashboard Cite

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Relaxed Constant Positive Linear Dependence Constraint Qualification for Disjunctive Systems

2023

Set-Valued Var. Anal

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A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization

Mehlitz

2023

Optim Lett

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In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an explicit elementary computation of the so-called second subderivative of the indicator function associated with the semidefinite cone which recovers the best curvature term known in the literature.

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Second order variational analysis of disjunctive constraint sets and its applications to optimization problems

Cited by 3 publications

References 34 publications

Relaxed constant positive linear dependence constraint qualification for disjunctive programs

Relaxed constant positive linear dependence constraint qualification for disjunctive programs

Relaxed Constant Positive Linear Dependence Constraint Qualification for Disjunctive Systems

A simple proof of second-order sufficient optimality conditions in nonlinear semidefinite optimization

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