ROA: Numerical Methods for Nonsmooth Optimization

9401119奥弗顿这项建议解决了NSF的研究机会奖计划的目标：使研究机构的研究人员与研究机会有限的研究人员在更知名的机构与NSF资助的研究人员合作。 本项目将把福德姆大学（纽约州布朗克斯）的一名同事带到纽约大学，与主要研究者建立合作工作关系。 研究了一类非光滑拟凸优化问题。 最小化目标是线性的，但约束是线性或非线性的Hermitian矩阵不等式。 一个等价的公式是埃尔米特定矩阵束的最大特征值的最小化，该矩阵束是一对矩阵（A，B），其中B正定。 这一特定问题在现代鲁棒控制方法中具有重要意义。 我们的目标是开发快速，可靠的数值算法来解决这个问题，以及分析有关最优性条件和算法收敛性的理论问题。 将开发软件并通过互联网（使用Netlib）提供给一般科学界。 将强调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. ***