Journal ArticleDOI
The limiting Lagrangian as a consequence of Helly's theorem
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The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs as mentioned in this paper.Abstract:
The perturbational Lagrangian equation established by Jeroslow in convex semi-infinite programming is derived from Helly's theorem and some prior results on one-dimensional perturbations of convex programs.read more
Citations
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Semi-Infinite Programming
Marco A. López,Georg Still +1 more
TL;DR: Semi-infinite programming (SIP) as discussed by the authors is an optimization problem in which finitely many variables appear in infinitely many constraints, and it naturally arises in an abundant number of applications in different fields of mathematics, economics and engineering.
Book
Semi-Infinite Programming and Applications
TL;DR: An important list of topics in the physical and social sciences involves continuum concepts and modelling with infinite sets of inequalities in a finite number of variables, including engineering design, variational inequalities and saddle value problems, and fuzzy set theory.
From linear to convex systems: consistency, Farkas' Lemma and applications
TL;DR: In this paper, the authors presented a study partially supported by MCYT of Spain and FEDER of EU, Grant BMF2002-04114-676C02-01.
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Direct theorems in semi-infinite convex programming
TL;DR: It is shown that a semi-infinite quasi-convex program with certain regularity conditions possesses finitely constrained subprograms with the same optimal value.
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A primal-dual projection method for solving systems of linear inequalities
TL;DR: In this paper, a projection-type method is described for finding a feasible point for a system of linear inequalities, where the solution set has nonempty interior and termination occurs after a finite number of iterations.
References
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Journal ArticleDOI
Duality in Semi-Infinite Programs and some Works of Haar and Caratheodory
TL;DR: In this article, an extended dual theorem comparable in precision and exhaustiveness to the finite space theorem is developed for arbitrary convex programs with convex constraints which subsumes in principle all characterizations of optimality or duality in convex programming.
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An Infinite Linear Program with a Duality Gap
R. J. Duffin,L. A. Karlovitz +1 more
TL;DR: In this paper, a duality theorem for semi-infinite linear programs is proved for infinite programs with finite extrema, where the minimum of the former is not equal to the maximum of the latter, and the existence of such a gap indicates that Haar's statement needs qualification.
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Duality gaps in semi-infinite linear programming—an approximation problem
TL;DR: The key idea is to guarantee the approximation of the primal program by a sequence of linear programs where thenth approximating program is to minimize the objective function subject to the firstn constraints.
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Constructing a perfect duality in infinite programming
TL;DR: In this paper, a Fredholm type theorem of the alternative characterizes the set of all ascent vectors associated with an arbitrary system of linear inhomogeneous inequalities in a finite number of variables.
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Convex analysis treated by linear programming
TL;DR: The present approach uses the support planes of the constraint region to transform the standard convex program into an equivalent linear program, and the duality theory of infinite linear programming shows how to construct a new dual program of bilinear type.