ROA: Numerical Methods for Nonsmooth Optimization

9401119 Overton该提案解决了国家科学基金会研究机会奖计划的目标：使研究机会有限的机构的研究人员能够与更知名机构的国家科学基金会资助的研究人员合作。该项目将邀请福特汉姆大学（Bronx， NY）的一位同事到纽约大学与首席研究员建立合作关系。研究了一类非光滑拟凸优化问题。最小化目标是线性的，但约束是厄米矩阵不等式，线性或非线性。一个等价的公式是厄米定矩阵铅笔的最大特征值的最小化，厄米定矩阵铅笔是一对矩阵（a， B）， B是正定的。这一特殊问题在现代鲁棒控制方法中具有重要意义。目标是开发快速、可靠的数值算法来解决这一问题，同时分析有关最优性条件和算法收敛的理论问题。将开发软件，并通过互联网（使用Netlib）向一般科学界提供。重点介绍在鲁棒控制中的应用。＊＊＊

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. ***