Background -- Sequential Optimization -- Barrier-Function and Penalty-Function Methods -- Proximal Minimization -- The Forward-Backward Splitting Algorithm -- Operators -- Averaged and Paracontractive Operators -- Convex Feasibility and Related Problems -- Eigenvalue Bounds -- Jacobi and Gauss-Seidel Methods -- The SMART and EMML Algorithms -- Alternating Minimization -- The EM Algorithm -- Geometric Programming and the MART -- Variational Inequality Problems and Algorithms -- Set-Valued Functions in Optimization -- Fenchel Duality -- Compressed Sensing -- Appendix A: Bregman-Legendre Functions.
Summary
"This book covers iterative optimization methods that stems from inverse problems and related issues. The author presents the theoretical side of inverse methods and as a result ignores discrete problems, stochastic methods, and combinatorial optimization. The coverage moves from an introduction of auxiliary function methods to a discussion of several examples of auxiliary fixed (AF) point methods in optimization to consideration of related topics such as operator fixed point methods. A few problems have been scattered throughout the book so that it might be used in a special topics class on optimization at the graduate level"-- Provided by publisher