A computer graphics-based Decision Support System for multiple objective linear programming

In this paper we propose a computer-graphics based Decision Support System for multiple objective linear programming that builds on the VIG system (Visual Interactive Goal programming). The essential part of the VIG system is Pareto Race, a dynamic and visual approach for exploring the efficient frontier of a multiple objective linear programming problem. Our objective is to extend Pareto Race to large-scale multiple objective linear programming. The approach works with any efficient solutions that are in general not extreme point solutions. Interactive use of computer graphics plays a central role. The approach, the underlying theory, and an illustrative example are described.     

On numerical solution of hemivariational inequalities by nonsmooth optimization methods

In this paper we consider numerical solution of hemivariational inequalities (HVI) by using nonsmooth, nonconvex optimization methods. First we introduce a finite element approximation of (HVI) and show that it can be transformed to a problem of finding a substationary point of the corresponding potential function. Then we introduce a proximal budle method for nonsmooth nonconvex and constrained optimization. Numerical results of a nonmonotone contact problem obtained by the developed methods are also presented.