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. |
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... closed convex cone with interior S 2. Explain why S2 is not a polyhedron . ' ++ ' 3. ( S3 is not strictly convex ) Find nonzero matrices X and Y in S3 such that R + XR + Y and ( X + Y ) / 2 S3 + . ' ++ 4. ( A nonlattice ordering ) ...
... convexity , we need second order information to tell us more about minimizers . The following elementary result from ... closed and convex , and that the point y does not lie in C. Then there exist a real b and a nonzero element a of E ...
... closed convex cone . 2. ( Examples of normal cones ) For the following sets CC E , check C is convex and compute the normal cone Nc ( x ) for points ≈ in C : ( a ) C a closed interval in R. ( b ) CB , the unit ball . ( c ) C a subspace ...
... convex then it has at most one global minimizer on C. ( b ) Prove the function f ( x ) = || xy || 2/2 is strictly convex on E for any point y in E. ( c ) Suppose C is a nonempty , closed convex subset of E. ( i ) If y is any point in E ...
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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 |