Mathematical Sciences: Eigenvalue Optimization and Robust Mathematical Programming

本课题将研究非线性规划中的特征值优化和鲁棒方法。特征值优化的研究将考虑谱半径映射的变分性质以及产生谱实部最大的映射。鲁棒全局算法和鲁棒局部理论利用凸复合函数的行为将得到发展。将特别注意允许放宽规则假设的技术。该研究在复杂化学过程建模、结构优化设计、反馈镇定和动力系统镇定等方面具有广泛的应用。

This project will study eigenvalue optimization and robust methods in nonlinear programming. The research on eigenvalue optimization will consider variational properties of the spectral radius map and the mapping that yields the maximum real part of the spectrum. Robust global algorithms and robust local theory using the behavior of convex composite functions will be developed. Particular attention will be given to techniques that permit the relaxation of regularity hypotheses. This research has applications in modeling complex chemical processes, optimal design of structures, feedback stabilization, and stabilization of dynamical systems.