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.
