Bøker i Applied Optimization-serien

The first elementary exposition of core ideas of complexity theory for convex optimization, this book explores optimal methods and lower complexity bounds for smooth and non-smooth convex optimization. Also covers polynomial-time interior-point methods.

Multicriteria analysis is a rapidly growing aspect of operations research and management science, with numerous practical applications in a wide range of fields. This book presents all the recent advances in multicriteria analysis, including multicriteria optimization, goal programming, outranking methods, and disaggregation techniques.

Collects papers that cover such areas as linear and nonlinear complementarity problems, variational inequality problems, nonsmooth equations and nonsmooth optimization problems, economic and network equilibrium problems, semidefinite programming problems, maximal monotone operator problems, and mathematical programs with equilibrium constraints.

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 our general approach possible we had to improve upon classical results like the Hölder-Minkowsky inequality of Lp. All the material is either new or very recent, and has never been organized in a book. Audience: This book will be of interest to both researchers in nonlinear analysis and to applied mathematicians dealing with numerical solution of integral equations, equilibrium problems, image reconstruction, optimal control, etc.