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A Face Algorithm for Linear Programming

Ping-Qi Pan(panpq***at***seu.edu.cn)

Abstract: The simplex algorithm moves on the underlying polyhedron, from vertex to vertex, until reaching an optimal vertex. In contrast, the proposed algorithm proceeds from face to face until reaching an optimal face along with a pair of primal and dual optimal solutions. The algorithm solves a single system in each iteration, compared with the simplex algorithm which solves four. It computes the search direction as an orthogonal projection of the negative objective gradient (for minimization) onto a relevant null space. Reported computational results are preliminary but very favorable.

Keywords: linear programming, level face, optimal face, Cholesky factorization, orthogonal projection

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Citation: Department of Mathematics, Southeast University, 210096, China, 10/2007

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Entry Submitted: 10/17/2007
Entry Accepted: 10/17/2007
Entry Last Modified: 10/17/2007

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