Some new Farkas-type results for inequality systems with DC functions

Boţ, Radu Ioan; Hodrea, Ioan Bogdan; Wanka, Gert

doi:10.1007/s10898-007-9159-8

Cited by 25 publications

(4 citation statements)

References 19 publications

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“…Very recently, an optimality condition for (1.1) was established in [41] for the case when f t are not necessary lsc, and a Lagrangian duality result via the interiority technique for (1.3) was established in [3] without any continuity assumption on f and g. Indeed, in the mathematical programming, many of the problems naturally involve non-convex and non-continuous functions. For example, in the DC infinite programming (see for example [7,19,20,21,22] and references therein), the objective functions and constraint functions are, in general, assumed to be DC functions (such a function is, by definition, a difference of two convex functions and so can be neither convex nor lsc). Another important example is the convex composite problem which has been studied extensively by many researchers (see [14,39,46,47,52] and references therein).…”

Section: 2)mentioning

confidence: 99%

Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming

Fang¹,

Li²,

Ng³

2010

SIAM J. Optim.

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Abstract. For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are consequence of the constrained system, and we provide necessary and/or sufficient conditions for a stable Farkas lemma to hold. Similarly, we provide characterizations for constrained minimization problems to have the strong or strong stable Lagrangian dualities. Several known results in the conic programming problem are extended and improved.

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Section: 2)mentioning

confidence: 99%

Constraint Qualifications for Extended Farkas's Lemmas and Lagrangian Dualities in Convex Infinite Programming

Fang¹,

Li²,

Ng³

2010

SIAM J. Optim.

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“…Therefore one could try to use techniques coming from dc programming techniques (cf. [2]) in order to deal with duality in this case.…”

Section: Future Researchmentioning

confidence: 99%

Duality for Linear Chance-Constrained Optimization Problems

Boţ¹,

Lorenz²,

Wanka³

2010

Journal of the Korean Mathematical Society

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Abstract. In this paper we deal with linear chance-constrained optimization problems, a class of problems which naturally arise in practical applications in finance, engineering, transportation and scheduling, where decisions are made in presence of uncertainty. After giving the deterministic equivalent formulation of a linear chance-constrained optimization problem we construct a conjugate dual problem to it. Then we provide for this primal-dual pair weak sufficient conditions which ensure strong duality. In this way we generalize some results recently given in the literature. We also apply the general duality scheme to a portfolio optimization problem, a fact that allows us to derive necessary and sufficient optimality conditions for it.

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“…Since the difference of two convex functions is not necessarily a convex function, the problem ( p λ ) is a nonconvex programming problem. In order to construct the dual problem to ( p λ ), we will use an approach inspired by DC programming (see [13] or [3,5,8]) and deal with it as two cases.…”

Section: Preliminariesmentioning

confidence: 99%