Sensitivity Functionals in Convex Optimization Problem

Abstract

Lagrange multiplier method based o modified Lagrangian functionals is one of the main methods for solving the finite dimensional convex optimization problem. Recently the Lagrange multiplier method is successfully applied to the solution of infinite- dimensional variational inequalities in mechanics. Convergence of Lagrange multiplier method is provided with the help of property of lower semicontinuity of sensitivity function. It is possible to prove the continuous differentiability of dual function. It allows for the solution of a dual problem to apply effective gradient methods of maximizing. In our paper we investigate the Lagrange multiplier method in finite-dimensional convex optimization problem and in infinite-dimensional semicoercive Signorini's problem of mechanics.