Convergence and approximation for primal-dual methods in large-scale optimization

Abstract

Large-scale problems in convex optimization often can be reformulated in primal-dual (minimax) representations having special decomposition properties. Approximation of the resulting high-dimensional problems by restriction to low-dimensional subspaces leads to a family of minimax problems dependent on a parameter. The continuity and convergence properties of this dependence are explored in this dissertation. Examples in optimal control and stochastic programming are considered in which discretizations give rise to large-scale optimization problems. A possible approach to the numerical solution of the discretized problems is described, as well as details of its computer implementation.