Elementary Convexity with Optimization

This book develops the concepts of fundamental convex analysis and optimization by using advanced calculus and real analysis. Brief accounts of advanced calculus and real analysis are included within the book. The emphasis is on building a geometric intuition for the subject, which is aided further by supporting figures. Two distinguishing features of this book are the use of elementary alternative proofs of many results and an eclectic collection of useful concepts from optimization and convexity often needed by researchers in optimization, game theory, control theory, and mathematical economics. A full chapter on optimization algorithms gives an overview of the field, touching upon many current themes. The book is useful to advanced undergraduate and graduate students as well as researchers in the fields mentioned above and in various engineering disciplines.

Develops the concepts of fundamental convex analysis and optimization Emphasizes on the geometric intuition of convex analysis and optimization Uses elementary alternative proofs of many results and an eclectic collection of useful facts

Auteur

Vivek S. Borkar is former Institute Chair Professor with the Department of Electrical Engineering, Indian Institute of Technology Bombay, where he now continues as Emeritus Fellow. He obtained his B.Tech. from IIT Bombay, M.S. from Case Western Reserve University, and Ph.D. from the University of California, Berkeley. Earlier, he has held positions at TIFR-CAM and the Indian Institute of Science in Bengaluru and Tata Institute of Fundamental Research (TIFR), Mumbai, and visiting positions at the University of Twente, Massachusetts Institute of Technology, University of California at Berkeley, the University of Maryland at College Park, and the University of Illinois at Urbana-Champaign. His research interests include stochastic control and optimization, inclusive of theory, algorithms, and applications.

K. S. Mallikarjuna Rao is Professor with the Interdisciplinary Program in Industrial Engineering and Operations Research, Indian Institute of Technology Bombay, India. He completed his Ph.D. in Mathematics from the Indian Institute of Science, Bengaluru, India, in 2002 and M.Sc. in Mathematics form Andhra University, Visakhapattanam, India. Earlier, he held postdoctoral positions at the Universite de Provence, Marseille, France; the Indian Statistical Institute, Delhi, India; the University of Texas at Dallas, USA; and the TIFR-CAM, Bengaluru, India. His research interests are control theory, game theory, networks, probability, optimization, and mathematical finance.

Résumé

"Each chapter ... is followed by an interesting and useful set of exercises. ... this book constitutes a very valuable addition to the existing literature on convexity and optimization. It can be used as a textbook for undergraduate courses on these subjects." (Juan-Enrique Martínez-Legaz, zbMATH 1528.26001, 2024)

Contenu
Continuity and existence of optima.- Differentiability and local optimality.- Convex sets.- Convex functions.- Convex optimization.- Optimization algorithms: an overview.- Epilogue.