Algorithmic Enhancements to the Method of Centers for Linear Programming Problems

• Published in: ORSA journal on computing Vol. 1; no. 3; pp. 159 - 171
• Main Authors: Boggs, Paul T., Domich, Paul D., Donaldson, Janet R., Witzgall, Christoph
• Format: Journal Article
• Language: English
• Published: INFORMS 01.08.1989
• Subjects: center trajectory; computers: software; dual affine direction; method of centers; multidirectional search direction; ordinary differential equations; programming: linear: algorithms, large scale systems; recentering; two-dimensional subproblem; two-step procedure
• ISSN: 0899-1499; 2326-3245
• DOI: 10.1287/ijoc.1.3.159

Interior point algorithms for solving linear programming problems are considered. The techniques are derived from a continuous version of Huard's method of centers that yields a family of trajectories in the feasible region that all converge to an optimal solution. The tangential direction of these trajectories is the dual affine direction. Deficiencies in some of these trajectories are discussed, and the need to recenter is argued. Several new algorithms that use the dual affine direction and a recentering direction in a multidirection approach are then derived. The most promising of these algorithms is based on minimizing the cost function on a sequence of two-dimensional cross sections of the feasible region. Numerical results are presented. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.