Computing B-Stationary Points of Nonsmooth DC Programs

Locating, characterizing and computing the stationary points of a function

A meth~ fi~r the hmalization, characterizadcm and ctnnputatitm of the stationary ptfints of a cxmtinutatsly differentiable real-valued fimction tff n variables is presented. It is based on the annbinatoriai topohgy concept of the degree of a mapping associated with an oriented polyhednm. The method consists of two principal steps: (i) Iocalizati, m (and am~putation if required) of a ~ationary p...

Double Bundle Method for Nonsmooth DC Optimization

The aim of this paper is to introduce a new proximal double bundle method for unconstrained nonsmooth DC optimization, where the objective function is presented as a difference of two convex (DC) functions. The novelty in our method is a new stopping procedure guaranteeing Clarke stationarity for solutions by utilizing only DC components of the objective function. This optimality condition is s...

Benchmark of Some Nonsmooth Optimization Solvers for Computing Nonconvex Proximal Points

The major focus of this work is to compare several methods for computing the proximal point of a nonconvex function via numerical testing. To do this, we introduce two techniques for randomly generating challenging nonconvex test functions, as well as two very specific test functions which should be of future interest to Nonconvex Optimization Benchmarking. We then compare the effectiveness of ...

Stationary Points and Equilibria

Almost all existence results in mathematical economics and game theory rely on some type of fixed point theorem. However, in many cases it is much easier to apply an equivalent stationary point theorem. In this survey paper we show for various general equilibrium and game theoretical models the usefulness of the stationary point approach to prove existence of equilibrium. We also consider path ...

Stationary Points of Transformation Groups.