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Nonlinear Optimization Nonlinear Optimization Andrzej Ruszczyn(cid:19)ski PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright '2006byPrincetonUniversityPress PublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,New Jersey08540 IntheUnitedKingdom: PrincetonUniversityPress,3MarketPlace,Wood- stock,Oxfordshire OX201SY AllRightsReserved LibraryofCongressCataloging-in-Publication Data Ruszczyn(cid:19)ski, AndrzejP. Nonlinearoptimization /AndrzejRuszczyn(cid:19)ski. p. cm. Includesbibliographical references andindex. ISBN-13: 978-0-691-11915-1 (acid-free paper) ISBN-10: 0-691-11915-5 (acid-free paper) 1. Mathematicaloptimization. 2. Nonlineartheories. I.Title. QA402.5.R872006 519.6(cid:150)dc22 2005049614 BritishLibraryCataloging-in-Publication Dataisavailable Thepublisher wouldliketoacknowledge theauthorofthisvolume forproviding thecamera-ready copyfromwhichthisbookwasprinted. Thisbookhasbeencomposed inTimesRomanandMathTimeusingLATEX. Printedonacid-free paper. 1 pup.princeton.edu PrintedintheUnitedStatesofAmerica 10987654321 to Darinka Wielez(cid:5) latczekac(cid:19) trzeba,nimsie(cid:7)przedmiots(cid:19)wiez(cid:5)y Jak(cid:12)gaucukruje,jaktytun(cid:19) ulez(cid:5)y? (cid:150)AdamMickiewicz,Dziady,Cze(cid:7)s(cid:19)c(cid:19) III Inhowfewyearsarefreshthemesmatured, As(cid:12)gsgrowcandiedortobaccocured? (cid:150)AdamMickiewicz,Forefathers’Eve,PartIII Contents Preface xi Chapter1. Introduction 1 PART1. THEORY 15 Chapter2. ElementsofConvexAnalysis 17 2.1 ConvexSets 17 2.2 Cones 25 2.3 ExtremePoints 39 2.4 ConvexFunctions 44 2.5 SubdifferentialCalculus 57 2.6 ConjugateDuality 75 Chapter3. OptimalityConditions 88 3.1 UnconstrainedMinimaofDifferentiableFunctions 88 3.2 UnconstrainedMinimaofConvexFunctions 92 3.3 TangentCones 98 3.4 OptimalityConditionsforSmoothProblems 113 3.5 OptimalityConditionsforConvexProblems 125 3.6 OptimalityConditionsforSmooth(cid:150)ConvexProblems 133 3.7 SecondOrderOptimalityConditions 139 3.8 Sensitivity 150 Chapter4. LagrangianDuality 160 4.1 TheDualProblem 160 4.2 DualityRelations 166 4.3 ConicProgramming 175 4.4 Decomposition 180 4.5 ConvexRelaxationofNonconvexProblems 186 4.6 TheOptimalValueFunction 191 4.7 TheAugmentedLagrangian 196 PART2. METHODS 209 Chapter5. UnconstrainedOptimizationofDifferentiableFunctions 211 5.1 IntroductiontoIterativeAlgorithms 211 5.2 LineSearch 213

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Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive t
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Nonlinear Optimization PDF

463 Pages·2006·1.94 MB·English
by  Andrzej Ruszczyński
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Nonlinear Optimization Nonlinear Optimization Andrzej Ruszczyn(cid:19)ski PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Copyright '2006byPrincetonUniversityPress PublishedbyPrincetonUniversityPress,41WilliamStreet,Princeton,New Jersey08540 IntheUnitedKingdom: PrincetonUniversityPress,3MarketPlace,Wood- stock,Oxfordshire OX201SY AllRightsReserved LibraryofCongressCataloging-in-Publication Data Ruszczyn(cid:19)ski, AndrzejP. Nonlinearoptimization /AndrzejRuszczyn(cid:19)ski. p. cm. Includesbibliographical references andindex. ISBN-13: 978-0-691-11915-1 (acid-free paper) ISBN-10: 0-691-11915-5 (acid-free paper) 1. Mathematicaloptimization. 2. Nonlineartheories. I.Title. QA402.5.R872006 519.6(cid:150)dc22 2005049614 BritishLibraryCataloging-in-Publication Dataisavailable Thepublisher wouldliketoacknowledge theauthorofthisvolume forproviding thecamera-ready copyfromwhichthisbookwasprinted. Thisbookhasbeencomposed inTimesRomanandMathTimeusingLATEX. Printedonacid-free paper. 1 pup.princeton.edu PrintedintheUnitedStatesofAmerica 10987654321 to Darinka Wielez(cid:5) latczekac(cid:19) trzeba,nimsie(cid:7)przedmiots(cid:19)wiez(cid:5)y Jak(cid:12)gaucukruje,jaktytun(cid:19) ulez(cid:5)y? (cid:150)AdamMickiewicz,Dziady,Cze(cid:7)s(cid:19)c(cid:19) III Inhowfewyearsarefreshthemesmatured, As(cid:12)gsgrowcandiedortobaccocured? (cid:150)AdamMickiewicz,Forefathers’Eve,PartIII Contents Preface xi Chapter1. Introduction 1 PART1. THEORY 15 Chapter2. ElementsofConvexAnalysis 17 2.1 ConvexSets 17 2.2 Cones 25 2.3 ExtremePoints 39 2.4 ConvexFunctions 44 2.5 SubdifferentialCalculus 57 2.6 ConjugateDuality 75 Chapter3. OptimalityConditions 88 3.1 UnconstrainedMinimaofDifferentiableFunctions 88 3.2 UnconstrainedMinimaofConvexFunctions 92 3.3 TangentCones 98 3.4 OptimalityConditionsforSmoothProblems 113 3.5 OptimalityConditionsforConvexProblems 125 3.6 OptimalityConditionsforSmooth(cid:150)ConvexProblems 133 3.7 SecondOrderOptimalityConditions 139 3.8 Sensitivity 150 Chapter4. LagrangianDuality 160 4.1 TheDualProblem 160 4.2 DualityRelations 166 4.3 ConicProgramming 175 4.4 Decomposition 180 4.5 ConvexRelaxationofNonconvexProblems 186 4.6 TheOptimalValueFunction 191 4.7 TheAugmentedLagrangian 196 PART2. METHODS 209 Chapter5. UnconstrainedOptimizationofDifferentiableFunctions 211 5.1 IntroductiontoIterativeAlgorithms 211 5.2 LineSearch 213

Description:
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive t
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