Sensitivity function: Properties and applications

The sensitivity function induced by a convex programming problem is examined. Its monotonicity, subdifferentiability, and closure properties are analyzed. A relation to the Pareto optimal solution set of the multicriteria convex optimization problem is established. The role of the sensitivity function in systems describing optimization problems is clarified. It is shown that the solution of these systems can often be reduced to the minimization of the sensitivity function on a convex set. Numerical methods for solving such problems are proposed, and their convergence is proved.