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
Results 1-5 of 36
... Order Conditions 166 172 8 Fixed Points 179 8.1 The Brouwer Fixed Point Theorem . 179 8.2 Selection and the Kakutani - Fan Fixed Point Theorem 190 8.3 Variational Inequalities . 200 9 More Nonsmooth Structure 213 9.1 Rademacher's ...
... order necessary optimality conditions for a local minimizer of a function subject to constraints . In that case ... order condition above is sufficient for x to be a global minimizer of ƒ on C. Proposition 2.1.2 ( First order sufficient ...
... order conditions , con- sider the framework of Corollary 2.1.3 ( First order conditions for linear constraints ) in the case E = R " , and suppose Vƒ ( x ) Є A * Y and ƒ is twice continuously differentiable near . If x is a local ...
... order conditions for linear constraints ) . 5. Prove that the differentiable function x2 + x2 ( 1 − x1 ) 3 has a unique critical point in R2 , which is a local minimizer , but has no global minimizer . Can this happen on R ? 6. ( The ...
... order conditions for linear constraints ) to find the solution . ( The solution is called the BFGS update of C - 1 under the secant condition Xs = y . ) ( See also [ 61 , p . 205 ] . ) 14 . ** Suppose intervals I1 , I2 , ... , In CR are ...
Contents
1 | |
15 | |
Chapter 3 Fenchel Duality | 33 |
Chapter 4 Convex Analysis | 65 |
Chapter 5 Special Cases | 97 |
Chapter 6 Nonsmooth Optimization | 123 |
Chapter 7 KarushKuhnTucker Theory | 153 |
Chapter 8 Fixed Points | 179 |
Chapter 9 More N onsmooth Structure | 213 |
Infinite Versus Finite Dimensions | 239 |
Chapter 11 List of Results and Notation | 253 |
Bibliography | 275 |
Index | 289 |
Other editions - View all
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan M. Borwein,Adrian S. Lewis No preview available - 2000 |