On relations between chance constrained and penalty function problems under discrete distributions

Branda, Martin

doi:10.1007/s00186-013-0428-7

Cited by 7 publications

(6 citation statements)

References 21 publications

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“…Proof. The proof is analogous to Theorem 3 proposed by Branda [18] if we realize that the GMFCQ together with differentiability implies calmness of the problem (5) and that the local solution of (5) is permanently feasible.…”

Section: An Asymptotic Equivalence Of Stochastic Programming Problemsmentioning

confidence: 65%

“…It can be even shown that under mild conditions the penalty approach and the chance constrained problem are asymptotically equivalent; see Branda [14,15], Branda and Dupačová [16], and Ermoliev et al [17]. Recently, the equivalence was stated under exact penalization where a finite penalty parameter is sufficient to obtain a local optimal solution which is permanently feasible with respect to the random constraints; see Branda [18]. The exact penalization property is ensured by a very general calmness property of the underlying optimization problem; compare Burke [19,20], Clarke [21].…”

Section: Advances In Decision Sciencesmentioning

confidence: 99%

“…which is necessary for further steps and to show the asymptotic equivalence of the considered stochastic programming problems; compare Branda [18]. An important role is put to the problem where all random constraints are fulfilled.…”

Section: Problem Statementmentioning

confidence: 99%

“…Proposition 8. Calmness of the constraints system (15) at (0, * ) is equivalent to the existence of a local error bound: (18) for some constants̃> 0 and > 0.…”

Section: Definition 3 Letmentioning

confidence: 99%

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Exact Penalization in Stochastic Programming—Calmness and Constraint Qualification

Branda

2014

Advances in Decision Sciences

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We deal with the conditions which ensure exact penalization in stochastic programming problems under finite discrete distributions. We give several sufficient conditions for problem calmness including graph calmness, existence of an error bound, and generalized Mangasarian-Fromowitz constraint qualification. We propose a new version of the theorem on asymptotic equivalence of local minimizers of chance constrained problems and problems with exact penalty objective. We apply the theory to a problem with a stochastic vanishing constraint.

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Section: An Asymptotic Equivalence Of Stochastic Programming Problemsmentioning

confidence: 65%

Section: Advances In Decision Sciencesmentioning

confidence: 99%

Section: Problem Statementmentioning

confidence: 99%

“…Proposition 8. Calmness of the constraints system (15) at (0, * ) is equivalent to the existence of a local error bound: (18) for some constants̃> 0 and > 0.…”

Section: Definition 3 Letmentioning

confidence: 99%

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Exact Penalization in Stochastic Programming—Calmness and Constraint Qualification

Branda

2014

Advances in Decision Sciences

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“…This latter work is similar to those just discussed, since once more the analysis is based on the above inequalities and the sample size depends on the size of the feasible region. More recently, [45] investigated the relations between chance constrained and penalty function problems under discrete distributions. This analysis extended a number of previous works that analysed this relation under continuous distribution.…”

Section: Related Workmentioning

confidence: 99%

Confidence-based reasoning in stochastic constraint programming

Rossi

Hnich

Tarim

et al. 2015

Artificial Intelligence

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In this work we introduce a novel approach, based on sampling, for finding assignments that are likely to be solutions to stochastic constraint satisfaction problems and constraint optimisation problems. Our approach reduces the size of the original problem being analysed; by solving this reduced problem, with a given confidence probability, we obtain assignments that satisfy the chance constraints in the original model within prescribed error tolerance thresholds. To achieve this, we blend concepts from stochastic constraint programming and statistics. We discuss both exact and approximate variants of our method. The framework we introduce can be immediately employed in concert with existing approaches for solving stochastic constraint programs. A thorough computational study on a number of stochastic combinatorial optimisation problems demonstrates the effectiveness of our approach.

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