Linear Semi-Infinite Optimization
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Beschreibung
A linear semi-infinite program is an optimization problem withlinear objective functions and linear constraints in which eitherthe number of unknowns or the number of constraints is finite. Themany direct applications of linear semi-infinite optimization (orprogramming) have prompted considerable and increasing researcheffort in recent years. The authors' aim is to communicate the maintheoretical ideas and applications techniques of this fascinatingarea, from the perspective of convex analysis. The four sections ofthe book cover:
* Modelling with primal and dual problems - the primal problem,space of dual variables, the dual problem.
* Linear semi-infinite systems - existence theorems, alternativetheorems, redundancy phenomena, geometrical properties of thesolution set.
* Theory of linear semi-infinite programming - optimality, duality,boundedness, perturbations, well-posedness.
* Methods of linear semi-infinite programming - an overview of themain numerical methods for primal and dual problems.
Exercises and examples are provided to illustrate both theory andapplications. The reader is assumed to be familiar with elementarycalculus, linear algebra and general topology. An appendix onconvex analysis is provided to ensure that the book isself-contained. Graduate students and researchers wishing to gain adeeper understanding of the main ideas behind the theory of linearoptimization will find this book to be an essential text.
Autor*in
Miguel A. Goberna
Themen in »Linear Semi-Infinite Optimization«
Discrete Mathematics Diskrete Mathematik Lineare Optimierung Mathematics Mathematik Semiinfinite Optimierung