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Exact Penalty Functions for Nonlinear Integer Programming Problems

Author

Listed:
  • S. Lucidi

    (Sapienza University of Rome)

  • F. Rinaldi

    (Sapienza University of Rome)

Abstract

In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a continuous space.

Suggested Citation

  • S. Lucidi & F. Rinaldi, 2010. "Exact Penalty Functions for Nonlinear Integer Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 479-488, June.
    • Handle: RePEc:spr:joptap:v:145:y:2010:i:3:d:10.1007_s10957-010-9700-7
    DOI: 10.1007/s10957-010-9700-7
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    References listed on IDEAS

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    1. W. X. Zhu, 2003. "Penalty Parameter for Linearly Constrained 0–1 Quadratic Programming," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 229-239, January.
    2. Walter Murray & Kien-Ming Ng, 2010. "An algorithm for nonlinear optimization problems with binary variables," Computational Optimization and Applications, Springer, vol. 47(2), pages 257-288, October.
    3. Panos M Pardalos & Oleg A Prokopyev & Stanislav Busygin, 2006. "Continuous Approaches for Solving Discrete Optimization Problems," International Series in Operations Research & Management Science, in: Gautam Appa & Leonidas Pitsoulis & H. Paul Williams (ed.), Handbook on Modelling for Discrete Optimization, chapter 0, pages 39-60, Springer.
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    Citations

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    Cited by:

    1. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2013. "A new class of functions for measuring solution integrality in the Feasibility Pump approach: Complete Results," DIAG Technical Reports 2013-05, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    2. Filippo Fabiani & Barbara Franci, 2023. "On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 298-309, October.
    3. Md Saiful Islam & Md Sarowar Morshed & Md. Noor-E-Alam, 2022. "A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3023-3041, November.
    4. Anurag Jayswal & Sarita Choudhury, 2016. "An Exact Minimax Penalty Function Method and Saddle Point Criteria for Nonsmooth Convex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 179-199, April.
    5. Marianna De Santis & Stefano Lucidi & Francesco Rinaldi, 2010. "Feasibility Pump-Like Heuristics for Mixed Integer Problems," DIS Technical Reports 2010-15, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    6. Marianna De Santis & Sven de Vries & Martin Schmidt & Lukas Winkel, 2022. "A Penalty Branch-and-Bound Method for Mixed Binary Linear Complementarity Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 3117-3133, November.
    7. Stefano Lucidi & Francesco Rinaldi, 2010. "An Exact Penalty Global Optimization Approach for Mixed-Integer Programming Problems," DIS Technical Reports 2010-17, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".
    8. Ma, Cheng & Zhang, Liansheng, 2015. "On an exact penalty function method for nonlinear mixed discrete programming problems and its applications in search engine advertising problems," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 642-656.
    9. Hager, William W. & Hungerford, James T., 2015. "Continuous quadratic programming formulations of optimization problems on graphs," European Journal of Operational Research, Elsevier, vol. 240(2), pages 328-337.
    10. Dominik Garmatter & Margherita Porcelli & Francesco Rinaldi & Martin Stoll, 2023. "An improved penalty algorithm using model order reduction for MIPDECO problems with partial observations," Computational Optimization and Applications, Springer, vol. 84(1), pages 191-223, January.
    11. M. Santis & F. Rinaldi, 2012. "Continuous Reformulations for Zero–One Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 75-84, April.
    12. Marianna De Santis & Francesco Rinaldi, 2010. "Continuous reformulations for zero-one programming problems," DIS Technical Reports 2010-16, Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza".

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