A new approach to nonconvex optimization

In this paper we propose a new approach based on global optimality conditions for solving continuous nonconvex optimization problems. We present in detail a technique for finding a solution to the following three problems: the problem of polyhedral separability, the problem of solving a system of nonlinear equations, and the problem of finding the Nash equilibrium point in bimatrix games by means of the variational approach using the global search methodology. This work was supported by the Russian Foundation for Basic Research (project No. 05-01-00110) and by the grant of President of Russia (No. MK-6580.2006.1).