On Tuesday, April 18, 2017 -  Metro Data, Inc.'s Chief of Network Operations, Dr. Michael Orlitzky, will present a colloquium on Lyapunov rank in conic optimization at Towson University, Mathematics Department.

Abstract: Many people are familiar with the classical linear programming problem (LP) that is used to solve scheduling, allocation, and navigation problems.

Any optimal solution to (LP) will satisfy a “complementary slackness” condition, which can be used to solve (LP).

Conic programming replaces the non-negativity constraints in (LP) with certain cone constraints. Conic programming can be used to solve harder problems, like robust linear programs, max-cut, and non-convex quadratic minimization problems. Optimal solutions to conic programs also satisfy a complementary slackness condition, but that condition may not decompose into a linear system of equations of full rank.

How many equations do we get? The answer to that question is called the Lyapunov rank of the cone.  We introduce the concept and some recent results.