Simple Bounds for Solutions of Monotone Complementarity Problems and Convex Programs

摘要

For a solvable monotone complementarity problem it is shown that each feasible point which is not a solution of the problem provides simple numerical bounds for some or all components of all solution vectors. Consequently for a solvable differentiable convex program each primal-dual feasible point which is not optimal provides simple numerical bounds for some or all components of all primal-dual solution vectors. Also given is existence result and simple bounds for solutions of monotone complementarity problems satisfying a new, distributed constraint qualification. This result carries over to a simple existence and boundedness result for differentiable convex programs satisfying a similar constraint qualification. (Author)