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. Graduate students, university teachers, and optimization practitioners in applied mathematics, engineering, and economics will find this book useful.