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A homotopy method for nonlinear semidefinite programming

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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.

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Acknowledgements

The authors are grateful to anonymous reviewers for many helpful suggestions.

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Authors and Affiliations

  1. Faculty of Management and Economics, Dalian University of Technology, Dalian, Liaoning, 116025, China

    Li Yang

  2. School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning, 116025, China

    Bo Yu

Authors
  1. Li Yang
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  2. Bo Yu
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Correspondence to Bo Yu.

Additional information

The research was supported by the National Natural Science Foundation of China (11171051, 91230103, 71172136) and Program for New Century Excellent Talents in University (NCET-10-0281).

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Yang, L., Yu, B. A homotopy method for nonlinear semidefinite programming. Comput Optim Appl 56, 81–96 (2013). https://doi.org/10.1007/s10589-013-9545-8

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