Approaches to the Theory of Optimization

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Cambridge University Press, Jun 3, 2004 - Mathematics - 220 pages
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Optimization is concerned with finding the best (optimal) solution to mathematical problems that may arise in economics, engineering, the social sciences and the mathematical sciences. As is suggested by its title, this book surveys various ways of penetrating the subject. The author begins with a selection of the type of problem to which optimization can be applied and the remainder of the book develops the theory, mainly from the viewpoint of mathematical programming. To prevent the treatment becoming too abstract, subjects which may be considered 'unpractical' are not touched upon. The author gives plausible reasons, without forsaking rigor, to show how the subject develops 'naturally'. Professor Ponstein has provided a concise account of optimization which should be readily accessible to anyone with a basic understanding of topology and functional analysis. Advanced students and professionals concerned with operations research, optimal control and mathematical programming will welcome this useful and interesting book.
 

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Contents

An intuitive approach to mathematical programming
11
A global approach by bifunctions
30
A global approach by conjugate duality
84
A local approach for optimization problems in Banach
109
Some other approaches
131
Some applications
153
Appendix A
176
References
196
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Page 196 - Necessary optimality criteria in mathematical programming in the presence of differentiability.
Page 200 - Taylor, Peter D. : Subgradients of a convex function obtained from a directional derivative. Pacific J. Math. 44, 739-747 (1973).
Page 200 - RT ROCKAFELLAR, Monotone operators and the proximal point algorithm, SIAM J. Control Opt., 14 (1976), pp.
Page 196 - Zlobec. S. (1976). Characterization of optimality in convex programming without a constraint qualification. JOTA 20, 417-37.
Page 200 - A saddle-point optimality criterion for nonconvex programming in normed spaces. SIAM J. appl. Math. 23, 203-13.

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