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A bstmct Given a set n of Er' and a function f : n -+ Rn the problem of finding a point x' E n such that (x x·)tf(x·) 2: 0 for any x E n is referred to as a stationary point problem and x· is called a stationary point. For the problem with conical n and strongly copositive f we propose a system of equations whose solution set contains a path connecting a trivial starting point to a stationary point. We also develop an algorithm to trace the path when f is an affine function with a copositive plus matrix. Starting with an appropriate point the algorithm provides a stationary point or shows that there exist no stationary points.

THE PATH FOLLOWING ALGORITHM FOR STATIONARY POINT PROBLEMS ON POLYHEDRAL CONES