Introduction to Optimization and Semidifferential Calculus

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SIAM, May 3, 2012 - Mathematics - 353 pages
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This text provides a modern and mathematically rigorous treatment of semidifferential calculus in the context of optimization. Semidifferentials are a natural tool for solving certain problems in non-differentiable optimization. Classical notions in convex analysis are introduced (convexification, duality, linear and quadratic programming, two-person zero-sum games, Lagrange primal and dual problems, semiconvex and semiconcave functions) and the theory is developed to a sophisticated enough level to tackle finite-dimensional versions of problems in the calculus of variations. This text is designed for a one-term course at the undergraduate level in a wide variety of numerate disciplines and includes sufficient background material in calculus and linear algebra to be self-contained. Additional material beyond the scope of a basic undergraduate course is included to further develop the theory. The theoretical content of the text is enriched by numerous examples and exercises, for which solutions are included.
 

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Contents

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About the author (2012)

M. C. Delfour is a Professor of Mathematics and Statistics at the University of Montreal in Canada, a member of the Canadian Academy of Sciences (FRSC), a SIAM fellow and a former Guggenheim and Killam Fellow. He is a former president of the Canadian Mathematical Society and has served on numerous Canadian and international advisory boards and committees. He has been a Professional Engineer (PEng) since 1966 and is the author or co-author of 13 books and more than 165 papers.

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