Elementary Convexity with Optimization

Vivek S. Borkar, K. S. Mallikarjuna Rao (Autoren)

Buch | Softcover

139 Seiten

2023 | 2023 ed.
Springer Verlag, Singapore
978-981-99-1651-1 (ISBN)

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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.

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.

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

Erscheinungsdatum	20.07.2023
Reihe/Serie	Texts and Readings in Mathematics
Zusatzinfo	2 Illustrations, color; 34 Illustrations, black and white
Verlagsort	Singapore
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
Themenwelt	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
Schlagworte	algorithms • conditions for optimality • Convexity • Duality • existence of optima • Optimization
ISBN-10	981-99-1651-8 / 9819916518
ISBN-13	978-981-99-1651-1 / 9789819916511
Zustand	Neuware