  


AN INEQUALITYCONSTRAINED SQP METHOD FOR EIGENVALUE OPTIMIZATION
Vyacheslav Kungurtsev(vyacheslav.kungurtsevcs.kuleuven.be) Abstract: We consider a problem in eigenvalue optimization, in particular find ing a local minimizer of the spectral abscissa  the value of a parameter that results in the smallest magnitude of the largest real part of the spectrum of a matrix system. This is an important problem for the stabilization of control sys tems. Many systems require the spectra to lie in the left half plane in order for stability to hold. The optimization problem, however, is difficult to solve because the underlying objective function is nonconvex, nonsmooth, and nonLipschitz. In addition, local minima tend to correspond to points of nondifferentiability and locally nonLipschitz behavior. We present a sequential linear and quadratic programming algorithm that solves a series of linear or quadratic subproblems formed by linearizing the surfaces corresponding to the largest eigenvalues. We present numerical results comparing the algorithms to the state of the art. Keywords: Robust control, stabilizing control, eigenvalue optimization, spectral abscissa, sequential quadratic programming, spectral optimization, nonlinear eigenvalue problem Category 1: Applications  Science and Engineering (Control Applications ) Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Submitted to ESAIM Download: [PDF] Entry Submitted: 05/09/2014 Modify/Update this entry  
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