Semi-infinite programming

López, Marco A.; Still, Georg J.

doi:10.1016/j.ejor.2006.08.045

Cited by 280 publications

(179 citation statements)

References 69 publications

(70 reference statements)

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“…In this context there are several promising algorithms that could be used to perform robust optimization on the surrogate model. It should be noted that solving (2) is equivalent to solving a semi-infinite optimization problem (López and Still 2007) since (2) can be written as a constrained minimization problem over an infinite number of constraints. For a survey of the state of the art methods that solve (2) via a semi-infinite programming approach please refer to (Stein 2012).…”

Section: Robust Optimization Of Unconstrained Problems Affected By Pamentioning

confidence: 99%

Efficient global robust optimization of unconstrained problems affected by parametric uncertainties

Rehman

Langelaar

2015

Struct Multidisc Optim

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A novel technique for efficient global robust optimization of problems affected by parametric uncertainties is proposed. The method is especially relevant to problems that are based on expensive computer simulations. The globally robust optimal design is obtained by searching for the best worst-case cost, which involves a nested min-max optimization problem. In order to reduce the number of expensive function evaluations, we fit response surfaces using Kriging and use adapted versions of expected improvement to direct the search for the robust optimum. The numerical performance of the algorithm is compared against other techniques for min-max optimization on established test problems. The proposed approach exhibits reliable convergence, is more efficient than previous methods and shows strong scalability.

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Section: Robust Optimization Of Unconstrained Problems Affected By Pamentioning

confidence: 99%

Efficient global robust optimization of unconstrained problems affected by parametric uncertainties

Rehman

Langelaar

2015

Struct Multidisc Optim

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“…It has been well recognized in semi-infinite programming that the Extended MangasarianJilromovitz Constraint Qualification (EMFCQ), first introduced in [18], is particularly useful when the index set T is a compact subset of a finite-dimensional space and when g(x, t) := 9t(x) E C(T) for each x E X; see, e.g., [2,7,17,15,19,21,26,28,29] for various applications of the EMFCQ in semi-infinite programming. Without the compactness of the index set T and the continuity of the inequality constraint function g(x, t) with respect to the index variable t, problem (1.1) changes dramatically and-as shown belowdoes not allow us to employ the EMFCQ condition anymore.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of SIP problems the EMFCQ was first introduced in [18] and then extensively studied and applied in semi-infinite frameworks with X = IRm and Y = IRn; see, e.g., [15,19,21,27], where the reader can find its relationships with other constraint qualifications for SIP problems.…”

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confidence: 99%

Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs

Mordukhovich

Nghia

2013

Math. Program.

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Abstract. The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensional spaces of decision variables and contain infinitely many of equality and inequality constraints with arbitrary (may not be compact) index sets. These problems reduce to semi-infinite programs in the case of finite-dimensional spaces of decision variables. We extend the classical MangasarianFromovitz and Farkas-Minkowski constraint qualifications to such infinite and semi-infinite programs. The new qualification conditions are used for efficient computing the appropriate normal cones to sets of feasible solutions for these programs by employing advanced tools of variational analysis and generalized differentiation. In the further development we derive first-order necessary optimality conditions for infinite and semi-infinite programs, which are new in both finite-dimensional and infinite-dimensional settings.

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“…In the SIP literature, there exist two main approaches to the constraints set's substitution: discretization and reduction (see [10,20] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

“…Since that time the interest to SIP is constantly growing due to many important applications, both theoretical and practical. The information about history of SIP, its theoretical and numerical aspects, and the references can be found in [8,10,20,24,26].…”

Section: Introductionmentioning

confidence: 99%

Convex SIP Problems with Finitely Representable Compact Index Sets: Immobile Indices and the Properties of the Auxiliary NLP Problem

Kostyukova

Tchemisova

2015

Set-Valued Var. Anal

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In the paper, we consider a problem of convex Semi-Infinite Programming with a compact index set defined by a finite number of nonlinear inequalities. While studying this problem, we apply the approach developed in our previous works and based on the notions of immobile indices, the corresponding immobility orders and the properties of a specially constructed auxiliary nonlinear problem. The main results of the paper consist in the formulation of sufficient optimality conditions for a feasible solution of the original SIP problem in terms of the optimality conditions for this solution in a specially constructed auxiliary nonlinear programming problem and in study of certain useful properties of this finite problem.

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Semi-infinite programming

Cited by 280 publications

References 69 publications

Efficient global robust optimization of unconstrained problems affected by parametric uncertainties

Efficient global robust optimization of unconstrained problems affected by parametric uncertainties

Constraint qualifications and optimality conditions for nonconvex semi-infinite and infinite programs

Convex SIP Problems with Finitely Representable Compact Index Sets: Immobile Indices and the Properties of the Auxiliary NLP Problem

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