Linear and quadratic programming in oriented matroids

Abstract

We prove constructively duality theorems of linear and quadratic programming in the combinatorial setting of oriented matroids. One version of our algorithm for linear programming has the interesting feature of maintaining feasibility. The development of the quadratic programming duality result suggests the study of properties of square matrices such as symmetry and positive semi-definiteness in the context of oriented matroids.

DOI: 10.1016/0095-8956(85)90042-5

Cite this paper

@article{Todd1985LinearAQ, title={Linear and quadratic programming in oriented matroids}, author={Michael J. Todd}, journal={J. Comb. Theory, Ser. B}, year={1985}, volume={39}, pages={105-133} }