ROA: Numerical Methods for Nonsmooth Optimization

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9401119 Overton This proposal addresses the goal of NSF's Research Opportunity Award program: to enable researchers at institutions with limited research opportunities to work with NSF-funded investigators at better known institutions. This project will bring a colleague on the faculty of Fordham University (Bronx, NY) to New York University to develop a collaborative working relationship with the principal investigator. The work concerns a nonsmooth quasiconvex optimization problem. The minimization objective is linear, but the constraints are Hermitian matrix inequalities, either linear or nonlinear. An equivalent formulation is the minimization of the largest eigenvalue of a Hermitian definite matrix pencil, which is a pair of matrices (A, B) with B positive definite. This specific problem is of great importance in modern methods for robust control. The goal is the development of fast, reliable numerical algorithms to solve this problem, together with analysis of theoretical questions concerning optimality conditions and algorithm convergence. Software will be developed and made available to the general scientific community over the Internet (using Netlib). Applications in robust control will be emphasized. ***