Linear semi-infinite optimization
著者
書誌事項
Linear semi-infinite optimization
（Mathematical methods in practice, vol. 2）
Wiley, c1998
大学図書館所蔵 全12件
注記
Includes bibliographical references and index
内容説明・目次
内容説明
A linear semi-infinite program is an optimization problem with linear objective functions and linear constraints in which either the number of unknowns or the number of constraints is finite. The many direct applications of linear semi-infinite optimization (or programming) have prompted considerable and increasing research effort in recent years. The authors' aim is to communicate the main theoretical ideas and applications techniques of this fascinating area, from the perspective of convex analysis. The four sections of the book cover:Modelling with primal and dual problems - the primal problem, space of dual variables, the dual problem. Linear semi-infinite systems - existence theorems, alternative theorems, redundancy phenomena, geometrical properties of the solution set. Theory of linear semi-infinite programming - optimality, duality, boundedness, perturbations, well-posedness. Methods of linear semi-infinite programming - an overview of the main numerical methods for primal and dual problems. Exercises and examples are provided to illustrate both theory and applications. The reader is assumed to be familiar with elementary calculus, linear algebra and general topology.
An appendix on convex analysis is provided to ensure that the book is self-contained. Graduate students and researchers wishing to gain a deeper understanding of the main ideas behind the theory of linear optimization will find this book to be an essential text.
目次
MODELLING. Modelling with the Primal Problem. Modelling with the Dual Problem. LINEAR SEMI-INFINITE SYSTEMS. Alternative Theorems. Consistency. Geometry. Stability. THEORY OF LINEAR SEMI-INFINITE PROGRAMMING. Optimality. Duality. Extremality and Boundedness. Stability and Well-Posedness. METHODS OF LINEAR SEMI-INFINITE PROGRAMMING. Local Reduction and Discretization Methods. Simplex-Like and Exchange Methods. Appendix. Symbols and Abbreviations. References. Index.
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