Semidefinite programming methods for min-max robust parameter design

A min-max re-formulation of the robust parameter design problem was introduced in [S. Mukhopadhyay and D. Chakraborty, "A computational algorithm for selecting robust designs in safety and quality critical processes," Sankhya B, 73, May 2011]. This formulation poses a computationally challenging problem: that of finding the min-max value of a polynomial in several variables. It has been recently shown that such an infinite min-max optimization can be solved using semi-definite programming techniques. In this article, a new semi-definite programming algorithm is proposed for solving the min-max formulation of the robust parameter design problem.