A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations

Abstract

This paper deals with a certain class of optimization methods, based on conservative convex separable approximations (CCSA), for solving inequality-constrained nonlinear programming problems. Each generated iteration point is a feasible solution with lower objective value than the previous one, and it is proved that the sequence of iteration points converges toward the set of Karush--Kuhn--Tucker points. A major advantage of CCSA methods is that they can be applied to problems with a very large number of variables (say 104--105) even if the Hessian matrices of the objective and constraint functions are dense.