Convex Analysis and Nonlinear Optimization: Theory and ExamplesSpringer Science & Business Media, 29 Haz 2013 - 273 sayfa Optimization 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. |
İçindekiler
Inequality Constraints | 15 |
Fenchel Duality | 33 |
Convex Analysis | 65 |
Special Cases | 97 |
Nonsmooth Optimization | 123 |
KarushKuhnTucker Theory | 153 |
Fixed Points | 179 |
Infinite Versus Finite Dimensions | 209 |
List of Results and Notation | 221 |
Bibliography | 241 |
| 253 | |
Diğer baskılar - Tümünü görüntüle
Convex Analysis and Nonlinear Optimization: Theory and Examples Jonathan Borwein,Adrian S. Lewis Sınırlı önizleme - 2010 |
Sık kullanılan terimler ve kelime öbekleri
Banach space biconjugation bounded Calculate Clarke subdifferential closed and convex closed convex cone Consider constraints continuous conv convex cone convex function convex set convex set CCE Corollary cusco deduce df(x Dini directional derivative duality gap Euclidean space example Exercise 12 Exercise 9 Exercises and Commentary Farkas lemma Fenchel duality finite fixed point Fréchet differentiable function f Gâteaux Gâteaux differentiable gi(x Hence interior Karush-Kuhn-Tucker Karush-Kuhn-Tucker conditions Lagrangian Lemma level sets limiting subdifferential linear map linear program locally Lipschitz lower semicontinuous matrix metric regularity Michel-Penot minimizer monotone multifunction necessary conditions nonempty nonsmooth nonzero norm normal cone optimal solution optimal value order conditions polar polyhedral primal proof Proposition Prove f Prove the function real function result Section 3.3 Semidefinite programming sequence shows strictly convex subdifferential subgradient sublinear subset subspace surjective tangent cone theorem variational inequality vector zero
