A homotopy method for nonlinear semidefinite programming

Authors:
Li Yang;Bo Yu
Affiliations:
Faculty of Management and Economics, Dalian University of Technology, Dalian, China 116025;School of Mathematical Sciences, Dalian University of Technology, Dalian, China 116025
Venue:
Computational Optimization and Applications
Year:
2013

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Abstract

In this paper, for solving the nonlinear semidefinite programming problem, a homotopy is constructed by using the parameterized matrix inequality constraint. Existence of a smooth path determined by the homotopy equation, which starts from almost everywhere and converges to a Karush---Kuhn---Tucker point, is proven under mild conditions. A predictor-corrector algorithm is given for numerically tracing the smooth path. Numerical tests with nonlinear semidefinite programming formulations of several control design problems with the data contained in COMPl e ib are done. Numerical results show that the proposed algorithm is feasible and applicable.