Totally Convex Functions for Fixed Points Computation and Infinite Dimensional OptimizationSpringer Science & Business Media, 2000 - 202 sivua The main purpose of this book is to present, in a unified approach, several algorithms for fixed point computation, convex feasibility and convex optimization in infinite dimensional Banach spaces, and for problems involving, eventually, infinitely many constraints. For instance, methods like the simultaneous projection algorithm for feasibility, the proximal point algorithm and the augmented Lagrangian algorithm are rigorously formulated and analyzed in this general setting and shown to be applicable to much wider classes of problems than previously known. For this purpose, a new basic concept, total convexity, is introduced. Its properties are deeply explored, and a comprehensive theory is presented, bringing together previously unrelated ideas from Banach space geometry, finite dimensional convex optimization and functional analysis. For making a general approach possible the work aims to improve upon classical results like the Holder-Minkowsky inequality of ℒp. |
Sisältö
Totally Convex Functions | 1 |
12 The Modulus of Total Convexity | 17 |
13 Total Versus Locally Uniform Convexity | 30 |
14 Particular Totally Convex Functions | 45 |
Computation of Fixed Points | 65 |
22 Totally Nonexpansive Families of Operators | 79 |
23 Stochastic Convex Feasibility Problems | 92 |
24 Applications in Particular Banach Spaces | 109 |
Infinite Dimensional Optimization | 129 |
32 Convergence of the Proximal Point Method | 138 |
33 The Basics of a Duality Theory | 145 |
34 An Augmented Lagrangian Method | 154 |
35 Unconstrained Convex Minimization | 171 |
| 189 | |
| 201 | |
Muita painoksia - Näytä kaikki
Totally Convex Functions for Fixed Points Computation and Infinite ... D. Butnariu,A.N. Iusem Rajoitettu esikatselu - 2012 |
Totally Convex Functions for Fixed Points Computation and Infinite ... D. Butnariu,A.N. Iusem Esikatselu ei käytettävissä - 2012 |
Totally Convex Functions for Fixed Points Computation and Infinite ... D. Butnariu,A.N. Iusem Esikatselu ei käytettävissä - 2011 |
Yleiset termit ja lausekkeet
according to Proposition algorithms applied augmented Lagrangian method Banach space bounded sets Bregman distance Bregman function computational continuously differentiable contradiction converges to zero converges weakly convex feasibility problem convex optimization convex set deduce defined Denote Dƒ(x Dƒ(y Dƒ(z dµ(w exists a positive family of operators finite function f Gâteaux derivative Hence Hilbert space holds implies infinite dimensional last inequality Lemma lim inf lim sup locally uniformly convex lower semicontinuous modulus of total negentropy nonempty nonexpansive with respect nonexpansivity pole nonnegative Observe optimal solution orbit positive real number primal optimization problem problem 3.9 prove proximal point method respect to f sequence x}EN sequentially consistent stochastic convex feasibility strictly convex subgradient method subsets Suppose totally convex functions totally nonexpansive operators Tw(x vƒ(x weak accumulation points weak convergence x}KEN x*+¹ y}EN
Suositut otteet
Sivu 197 - Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces, Israel J.
Sivu 198 - Kartsatos, Athanassios G. (ed.), Theory and applications of nonlinear operators of accretive and monotone type.
Sivu 194 - K. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings, Marcel Dekker, New York 1984.
Sivu 191 - A generalized proximal point algorithm for the variational inequality problem in a Hilbert space.
Sivu 191 - Browder, FE and Petryshyn, WV The solution by iteration of nonlinear functional equations in Banach spaces, Bull.
Sivu 193 - Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization,
Sivu 190 - HH Bauschke and JM Borwein. Legendre functions and the method of random Bregman projections.
Sivu 190 - Bregman, LM The relaxation method of finding the common points of convex sets and its application to the solution of problems in convex programming. USSR Computational Mathematics and Mathematical Physics 7 (1967) 200217.
Sivu 193 - A Parallel Projection Method for Finding a Common Point of a Family of Convex Sets,
Viitteet tähän teokseen
Inherently Parallel Algorithms in Feasibility and Optimization and their ... D. Butnariu,S. Reich,Y. Censor Rajoitettu esikatselu - 2001 |
Set-Valued Mappings and Enlargements of Monotone Operators Regina S. Burachik,Alfredo N. Iusem Rajoitettu esikatselu - 2007 |