Optimal value function in semi-infinite programming

Linear semi-infinite programming deals with the optimization of linear functionals on finite-dimensional spaces under infinitely many linear constraints. For such kind of programs, a positive duality gap can occur between them and their corresponding dual problems, which are linear programs posed on infinite-dimensional spaces. This paper exploits some recent existence theorems for systems of linear inequalities in order to obtain a complete classification of linear semi-infinite programming problems from the point of view of the duality gap and the viability of the discretization numerical approach. The elimination of the duality gap is also discussed. ᮊ 1999 Academic Press Ž .Ž .Ý Ý t t t t tgT t gT

show abstract

“…Ž . Ž w x D c , c g int M, which also guarantees the boundedness of F* c see 16 . and references therein .…”

Section: žmentioning

confidence: 90%

On Duality in Semi-Infinite Programming and Existence Theorems for Linear Inequalities

Goberna

López

1999

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…-In [31], by means of an appropriate use of the subdifferential mapping, the connections among duality theory, solvability properties, and convergence properties of sequences of discretized linear semi-infinite programs were made explicit.…”

Section: Research Contributionsmentioning

confidence: 99%

Marco A. López, a Pioneer of Continuous Optimization in Spain

et al. 2020

View full text Add to dashboard Cite

(since 2012) and Adjunct Professor of the Centre for Informatics and Applied Optimization (CIAO) at Federation University Australia (since 2013). In 2013 he was elected a Corresponding Member of the Spanish Royal Academy of Sciences. Marco López has been a teacher for several generations of Spanish mathematicians, and adviser or co-adviser of 18 PhD students in several branches of Operations Research (OR) such as semi-infinite programming, network flows, assignment problems, convex

show abstract

“…in other words, there exist a subsequence of optimal solutions of the problems P (T r ; c) converging to an optimal solution of P: Statement (i) was proved in [43]. Concerning (ii), (a) is in [165]; (b) in [88] (in [96], for convex in…nite-dimensional optimization); (c) in [90, §8.3], although the study of the relationship between discretizability and absence of duality gap started with A. Charnes, W. Cooper and K. Kortanek ([41], [42], [43]), R.J. Du¢ n and L.A. Karlovitz [58], among others; and (d) is Theorem 8.6 in [90].…”

Section: Dualitymentioning

confidence: 99%

Recent contributions to linear semi-infinite optimization

Goberna

López

2017

4OR-Q J Oper Res

Self Cite

View full text Add to dashboard Cite

This paper reviews the state-of-the-art in the theory of deterministic and uncertain linear semi-in…nite optimization, presents some numerical approaches to this type of problems, and describes a selection of recent applications in a variety of …elds. Extensions to related optimization areas, as convex semi-in…nite optimization, linear in…nite optimization, and multi-objective linear semi-in…nite optimization, are also commented.

show abstract

Optimal value function in semi-infinite programming

Cited by 25 publications

References 15 publications

On Duality in Semi-Infinite Programming and Existence Theorems for Linear Inequalities

On Duality in Semi-Infinite Programming and Existence Theorems for Linear Inequalities

Marco A. López, a Pioneer of Continuous Optimization in Spain

Recent contributions to linear semi-infinite optimization

Contact Info

Product

Resources

About