Convex Analysis and Nonlinear Optimization: Theory and ExamplesOptimization is a rich and thriving mathematical discipline. The theory underlying current computational optimization techniques grows ever more sophisticated. The powerful and elegant language of convex analysis unifies much of this theory. The aim of this book is to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. It can serve as a teaching text, at roughly the level of first year graduate students. While the main body of the text is self-contained, each section concludes with an often extensive set of optional exercises. The new edition adds material on semismooth optimization, as well as several new proofs that will make this book even more self-contained. |
From inside the book
... space and accessibility rather than history or appli- cation : convex analysis developed historically from the calculus of vari- ations , and has important applications in optimal ... Euclidean Spaces 1.2 Symmetric Matrices viii Preface.
... Euclidean Spaces We begin by reviewing some of the fundamental algebraic , geometric and analytic ideas we use throughout the book . Our setting , for most of the book , is an arbitrary Euclidean space E , by which we mean a finite ...
... Euclidean space Y , we call a map A : E → Y linear if any points x and z in E and any reals A and μ satisfy A ( x + μz ) = λAx + μAz . In fact any linear function from E to R has the form ( a , ) for some element a of E. Linear maps ...
... Euclidean space , the map A : E → Y is linear , and N ( A ) n0 + ( C ) is a linear subspace , prove AC is closed . Show this result can fail without the last assumption . ( f ) Consider another nonempty closed convex set DCE such that ...
... Euclidean space and the map A : E → F is linear , prove ri AC Ari C. 1.2 Symmetric Matrices Throughout most of this book our setting 8 1. Background.
Contents
7 | |
15 | |
Fenchel Duality | 33 |
Convex Analysis | 65 |
Special Cases | 97 |
Nonsmooth Optimization | 123 |
Fixed Points | 183 |
Infinite Versus Finite Dimensions | 209 |
List of Results and Notation | 221 |
Bibliography | 241 |
Other editions - View all
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |