9311621 Tseng This research comprises two parts. The first part concerns the study of certain error bounds for nonlinear programs, complementarity and variational inequality problems, and the solution of convex inclusions. Roughly speaking, an error bound is a bound on the distance from a point to the solution set that depends only on some error function evaluated at that point. The investigation will focus on, though not restricted to, error bounds in which the error function is related to the solution set. Such error bounds are of interest because they are the key to analyzing, under minimal assumptions on the problem, the rate of convergence of iterative methods based on fixed point iterations. The second part of the research concerns the design and the convergence analysis of iterative methods using the above error bounds. The methods to be studied include the gradient projection algorithm of Goldstein and of Levitin and Polyak, coordinate descent methods, the proximal point algorithm, operator-splitting methods, the affine-scaling algorithm for semi-finite linear programming, and new methods motivated by error bounds. ***
