### Optimization and Systems Theory Seminar

Friday September 26, 2008, 11.00-12.00, Room 3721, Lindstedtsvägen 25

Anders Forsgren, Department of Optimization and Systems Theory, KTH

E-mail: andersf@kth.se

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An elementary proof of optimality conditions for linear programming

Proving optimality conditions for linear programming is
straightforward, if one assumes that the problem is primal nondegenerate. The
general case, covering degeneracy, is less straightforward. Traditionally, one
makes use of either Farkas' lemma or of the simplex method with some
anti-cycling scheme. In this talk, we give an elementary proof of optimality
conditions for linear programming, built on a straightforward classical
perturbation of the constraints. The proof does not require either the use of
Farkas' lemma or the use of the simplex method. As a by-product, we also obtain
a proof of Farkas' lemma.

Calendar of seminars
*Last update: June 2, 2008 by
Marie Lundin.
*