DERIVING POTENTIAL FUNCTIONS VIA A SYMMETRY PRINCIPLE FOR NONLINEAR EQUATIONS

Parameterized homotopy equations that define paths through the interio r of the feasible region of a linear program are reformulated as gradi ent mappings, and a standard symmetry principle for nonlinear equation s is then used to derive associated potential functions. These functio ns are the Lagrangians of weighted logarithmic barrier problems. Prima l, dual and self-dual cases are considered, with emphasis on the situa tion when starting points are infeasible. (C) 1997 Elsevier Science B. V.