Deriving potential functions via a symmetry principle for nonlinear equations

Authors:
J. L. Nazareth
Affiliations:
Department of Pure and Applied Mathematics, Washington State University, Pullman, WA 99164-3113, USA and Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA
Venue:
Operations Research Letters
Year:
1997

Citing 3
Cited 0

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Abstract

Parameterized homotopy equations that define paths through the interior of the feasible region of a linear program are reformulated as gradient mappings, and a standard symmetry principle for nonlinear equations is then used to derive associated potential functions. These functions are the Lagrangians of weighted logarithmic barrier problems. Primal, dual and self-dual cases are considered, with emphasis on the situation when starting points are infeasible.