Optimality conditions in convex optimization : a finitedimensional view
 Author/Creator
 Dhara, Anulekha.
 Language
 English.
 Imprint
 Boca Raton, Fla. ; London : CRC Press, c2012.
 Physical description
 xviii, 426 p. : ill. ; 24 cm.
Access
Contributors
 Contributor
 Dutta, Joydeep.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 413421) and index.
 Contents

 What Is Convex Optimization? Introduction Basic concepts Smooth Convex Optimization Tools for Convex Optimization Introduction Convex Sets Convex Functions Subdifferential Calculus Conjugate Functions epsilonSubdifferential Epigraphical Properties of Conjugate Functions Basic Optimality Conditions using the Normal Cone Introduction Slater Constraint Qualification Abadie Constraint Qualification Convex Problems with Abstract Constraints MaxFunction Approach ConeConstrained Convex Programming Saddle Points, Optimality, and Duality Introduction Basic Saddle Point Theorem Affine Inequalities and Equalities and Saddle Point Condition Lagrangian Duality Fenchel Duality Equivalence between Lagrangian and Fenchel Duality: Magnanti's Approach Enhanced Fritz John Optimality Conditions Introduction Enhanced Fritz John Conditions Using the Subdifferential Enhanced Fritz John Conditions under Restrictions Enhanced Fritz John Conditions in the Absence of Optimal Solution Enhanced Dual Fritz John Optimality Conditions Optimality without Constraint Qualification Introduction Geometric Optimality Condition: Smooth Case Geometric Optimality Condition: Nonsmooth Case Separable Sublinear Case Sequential Optimality Conditions and Generalized Constraint Qualification Introduction Sequential Optimality: Thibault's Approach Fenchel Conjugates and Constraint Qualification Applications to Bilevel Programming Problems Representation of the Feasible Set and KKT Conditions Introduction Smooth Case Nonsmooth Case Weak Sharp Minima in Convex Optimization Introduction Weak Sharp Minima and Optimality Approximate Optimality Conditions Introduction epsilonSubdifferential Approach MaxFunction Approach epsilonSaddle Point Approach Exact Penalization Approach Ekeland's Variational Principle Approach Modified epsilonKKT Conditions DualityBased Approach to epsilonOptimality Convex SemiInfinite Optimization Introduction SupFunction Approach Reduction Approach Lagrangian Regular Point FarkasMinkowski Linearization Noncompact Scenario: An Alternate Approach Convexity in Nonconvex Optimization Introduction Maximization of a Convex Function Minimization of d.c. Functions Bibliography Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 Optimality Conditions in Convex Optimization explores an important and central issue in the field of convex optimization: optimality conditions. It brings together the most important and recent results in this area that have been scattered in the literaturenotably in the area of convex analysisessential in developing many of the important results in this book, and not usually found in conventional texts. Unlike other books on convex optimization, which usually discuss algorithms along with some basic theory, the sole focus of this book is on fundamental and advanced convex optimization theory. Although many results presented in the book can also be proved in infinite dimensions, the authors focus on finite dimensions to allow for much deeper results and a better understanding of the structures involved in a convex optimization problem. They address semiinfinite optimization problems; approximate solution concepts of convex optimization problems; and some classes of nonconvex problems which can be studied using the tools of convex analysis. They include examples wherever needed, provide details of major results, and discuss proofs of the main results.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Anulekha Dhara, Joydeep Dutta.
 ISBN
 9781439868225 (hbk.)
 1439868220 (hbk.)