9705672 Polyak ABSTRACT The main purpose of this proposal is to develop new aspects of the Nonlinear Rescaling (NR) theory and new methods, that are based on this theory, for solving constrained optimization problems. Developing software, which will take into account the special structure of unconstrained optimization problems typical for the NR approach is our second goal. Solving real world large scale nonlinear optimization problems is our third main target. The ability to solve large scale nonlinear optimization problems is critical in mechanics, structural engineering, optimal control, tomography, image recognition, power system optimization, and economics, to mention a few. Recently the NR type methods have been used with great success for solving very complex Truss Topology Design (TTD) problems. The TTD problems arise in structural optimization, in particular, in creating bridges, cantilevers, and inner skeletons of airplane wings capable of carrying external loads under different loading scenarios. Funding a structure, which is able to withstand external forces, have certain characteristics of rigidity and at the same time to have minimal cost is a typical large scale nonlinear constrained optimization problem. Our research is aimed to find efficient methods for solving such problems.
