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Linear stationary point problems on unbounded polyhedra. (English) Zbl 0784.90072

Summary: We propose a complementary pivoting algorithm for finding a stationary point of an affine function on an unbounded polyhedron. Under some mild conditions there is a piecewise linear path from an arbitrarily chosen point in the polyhedron leading to a solution of the problem. By exploiting fully the linearity of the problem, each linear piece of the path is followed in principle by making just one linear programming pivoting step.

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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