Optimization: Algorithms and Consistent Approximations (Applied Mathematical Sciences)
• Author(s): Elijah Polak
• Publisher: Springer
• Publication Date: June 20, 1997 (774 pages)
• ISBN13: 9780387949710  ISBN10: 0387949712
This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semiinfinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as pointtoset maps, the treatment of minmax problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semiinfinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for minmax problems, as well as the newly developed theory of consistent approximations and the treatment of semiinfinite optimization and optimal control problems in this framework.
This book presents the first treatment of optimization algorithms for optimal control problems with statetrajectory 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 epiconvergence and optimality functions in the construction of consistent approximations to infinite dimensional problems.
