Optimization - Algorithms and Consistent Approximations

This book covers algorithms and discretization procedures for the solution of nonlinear programming, semi-infinite optimization, and optimal control problems. Among the important features included are a theory of algorithms represented as point-to-set maps ; the treatment of finite- and infinite-dimensional min-max problems with and without constraints ; a theory of consistent approximations dealing with the convergence of approximating problems and master algorithms that call standard nonlinear programming algorithms as subroutines, which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints ; and the completeness with which algorithms are analyzed. Chapter 5 contains mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modem treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework. This book presents the first rigorous treatment of implementable optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution. It is also the first to make use of the concepts of epi-convergence and optimality functions in the construction of consistent approximations to infinite-dimensional problems. Graduate students, university teachers, and optimization practitioners in applied mathematics, engineering, and economics will find this book useful.