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Global convergence of a class new smooth penalty algorithm for constrained optimization problem

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Abstract

In this paper, a class of smooth penalty functions is proposed for constrained optimization problem. It is put forward based on \(L_p\), a smooth function of a class of exact penalty function \({\ell _p}~\left( {p \in (0,1]} \right) \). Based on the class of penalty functions, a penalty algorithm is presented. Under the very weak condition, a perturbation theorem is set up. The global convergence of the algorithm is derived. This result generalizes some existing conclusions. Finally, numerical experiments on two examples demonstrate the effectiveness and efficiency of our algorithm.

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References

  1. Auslender, A.: Penalty and barrier methods: a unified framework. SIAM J. Optim. 10(1), 211–230 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Auslender, A., Cominetti, R., Haddou, M.: Asymptotic analysis for penalty and barrier methods in convex and linear programming. Math. Oper. Res. 22(1), 43–62 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ben-Tal, A., Teboulle, M.: A smoothing technique for nondifferentiable optimization problems. In: Optimization: Proceedings of the Fifth French-German Conference Held in Castel-Novel (Varetz), France, Oct. 3–8, 1988, pp. 1–11. Springer (2006)

  4. Mangasarian, O., Chen, C.: A class of smoothing functions for nonlinear and mixed complementarity problems. Comput. Optim. Appl. 5(2), 97–138 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, C., Mangasarian, O.L.: Smoothing methods for convex inequalities and linear complementarity problems. Math. Program. 71(1), 51–69 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gonzaga, C.C., Castillo, R.A.: A nonlinear programming algorithm based on non-coercive penalty functions. Math. Program. 96, 87–101 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Pinar, M.Ç., Zenios, S.A.: On smoothing exact penalty functions for convex constrained optimization. SIAM J. Optim. 4(3), 486–511 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  8. Rubinov, A.M., Glover, B.M., Yang, X.: Decreasing functions with applications to penalization. SIAM J. Optim. 10(1), 289–313 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, C., Ma, C., Zhou, J.: A new class of exact penalty functions and penalty algorithms. J. Global Optim. 58(1), 51–73 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  10. Luo, Z.-Q., Pang, J.-S., Ralph, D.: Mathematical Programs with Equilibrium Constraints. Cambridge University Press, Cambridge (1996)

    Book  MATH  Google Scholar 

  11. Babacan, S.D., Mancera, L., Molina, R., Katsaggelos, A.K.: Non-convex priors in Bayesian compressed sensing. In: 2009 17th European Signal Processing Conference, pp. 110–114 (2009). IEEE

  12. Kloft, M., Brefeld, U., Laskov, P., Müller, K.-R., Zien, A., Sonnenburg, S.: Efficient and accurate \(\ell _p\)-norm multiple kernel learning. NIPS 22, 997–1005 (2009)

    Google Scholar 

  13. Zhang, C., Wang, J., Xiu, N.: Robust and sparse portfolio model for index tracking. J. Ind. Manag. Optim. 15(3), 1001–1015 (2019)

    MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors would like to express their sincere thanks to the editor and the anonymous reviewers for their helpful comments and suggestions to improve this paper.

Funding

This research was supported by Natural Science Foundation of Shandong Province (ZR2021MA066).

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Author notes

  1. Ruyu Wang and Daojin Song have contributed equally to this work.

Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255049, People’s Republic of China

    Wenling Zhao, Ruyu Wang & Daojin Song

Authors
  1. Wenling Zhao
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  2. Ruyu Wang
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  3. Daojin Song
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Correspondence to Wenling Zhao.

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Zhao, W., Wang, R. & Song, D. Global convergence of a class new smooth penalty algorithm for constrained optimization problem. J. Appl. Math. Comput. 69, 3987–3997 (2023). https://doi.org/10.1007/s12190-023-01911-6

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  • DOI: https://doi.org/10.1007/s12190-023-01911-6

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