Convergence properties of a class of exact penalty methods for semi-infinite optimization problems

Abstract

In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian–Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.

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Acknowledgements

We would like to thank the referees for their valuable and helpful comments on our manuscript.

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Correspondence to Qian Liu.

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The work in this paper was supported by the National Natural Science Foundation of China (11271233, 11271226).

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Ju, J., Liu, Q. Convergence properties of a class of exact penalty methods for semi-infinite optimization problems. Math Meth Oper Res 91, 383–403 (2020). https://doi.org/10.1007/s00186-019-00693-7

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Keywords

  • Exact penalty function
  • Semi-infinite programming
  • Convergence
  • Nonlinear programming