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001470115 001__ 1470115
001470115 003__ OCoLC
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001470115 0247_ $$a10.1007/978-981-99-1652-8$$2doi
001470115 035__ $$aSP(OCoLC)1388494164
001470115 040__ $$aEBLCP$$beng$$cEBLCP$$dYDX$$dGW5XE
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001470115 08204 $$a516.08$$223/eng/20230711
001470115 1001_ $$aBorkar, Vivek S.
001470115 24510 $$aElementary convexity with optimization /$$cVivek S. Borkar, K. S. Mallikarjuna Rao.
001470115 260__ $$aSingapore :$$bSpringer,$$c2023.
001470115 300__ $$a1 online resource (148 p.).
001470115 336__ $$atext$$btxt$$2rdacontent
001470115 337__ $$acomputer$$bc$$2rdamedia
001470115 338__ $$aonline resource$$bcr$$2rdacarrier
001470115 4901_ $$aTexts and Readings in Mathematics ;$$vv. 83
001470115 504__ $$aIncludes bibliographical references and index.
001470115 5050_ $$aIntro -- Preface -- References -- Contents -- 1 Continuity and Existence of Optima -- 1.1 Some Basic Real Analysis -- 1.2 Bolzano-Weierstrass Theorem -- 1.3 Existence of Optima -- 1.4 More on Continuous Functions -- 1.5 Exercises -- References -- 2 Differentiability and Local Optimality -- 2.1 Introduction -- 2.2 Notions of Differentiability -- 2.3 Conditions for Local Optimality -- 2.4 Danskin's Theorem -- 2.5 Parametric Monotonicity of Optimizers -- 2.6 Ekeland Variational Principle -- 2.7 Mountain Pass Theorem -- 2.8 Exercises -- References -- 3 Convex Sets -- 3.1 Introduction
001470115 5058_ $$a3.2 The Minimum Distance Problem -- 3.3 Separation Theorems -- 3.4 Extreme Points -- 3.5 The Shapley-Folkman Theorem -- 3.6 Helly's Theorem -- 3.7 Brouwer Fixed Point Theorem -- 3.8 Proof of Theorem 3.1 -- 3.9 Exercises -- References -- 4 Convex Functions -- 4.1 Basic Properties -- 4.2 Continuity -- 4.3 Differentiability -- 4.4 An Approximation Theorem -- 4.5 Convex Extensions -- 4.6 Further Properties of Gradients of Convex Functions -- 4.7 Exercises -- References -- 5 Convex Optimization -- 5.1 Introduction -- 5.2 Legendre Transform and Fenchel Duality -- 5.3 The Lagrange Multiplier Rule
001470115 5058_ $$a5.4 The Arrow-Barankin-Blackwell Theorem -- 5.5 Linear Programming -- 5.6 Applications to Game Theory -- 5.6.1 Min-Max Theorem -- 5.6.2 Existence of Nash Equilibria -- 5.7 Exercises -- References -- 6 Optimization Algorithms: An Overview -- 6.1 Preliminaries -- 6.2 Line Search -- 6.3 Algorithms for Unconstrained Optimization -- 6.4 Algorithms for Constrained Optimization -- 6.5 Special Topics -- 6.6 Other Directions -- 6.7 Exercises -- References -- 7 Epilogue -- 7.1 What Lies Beyond -- 7.2 Bibliographical Note -- References -- Index
001470115 506__ $$aAccess limited to authorized users.
001470115 520__ $$aThis 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.
001470115 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed July 11, 2023).
001470115 650_0 $$aConvex sets.
001470115 650_0 $$aMathematical optimization.
001470115 655_0 $$aElectronic books.
001470115 7001_ $$aRao, K. S. Mallikarjuna.
001470115 77608 $$iPrint version:$$aBorkar, Vivek S.$$tElementary Convexity with Optimization$$dSingapore : Springer,c2023$$z9789819916511
001470115 830_0 $$aTexts and readings in mathematics ;$$vv. 83.
001470115 852__ $$bebk
001470115 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-99-1652-8$$zOnline Access$$91397441.1
001470115 909CO $$ooai:library.usi.edu:1470115$$pGLOBAL_SET
001470115 980__ $$aBIB
001470115 980__ $$aEBOOK
001470115 982__ $$aEbook
001470115 983__ $$aOnline
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