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Surrogate Mathematical Programming

Author

Listed:
  • Harvey J. Greenberg

    (Southern Methodist University, Dallas, Texas)

  • William P. Pierskalla

    (Southern Methodist University, Dallas, Texas)

Abstract

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach.

Suggested Citation

  • Harvey J. Greenberg & William P. Pierskalla, 1970. "Surrogate Mathematical Programming," Operations Research, INFORMS, vol. 18(5), pages 924-939, October.
    • Handle: RePEc:inm:oropre:v:18:y:1970:i:5:p:924-939
    DOI: 10.1287/opre.18.5.924
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    Citations

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    Cited by:

    1. Thomas L. Magnanti, 2021. "Optimization: From Its Inception," Management Science, INFORMS, vol. 67(9), pages 5349-5363, September.
    2. Lorena, Luiz Antonio N. & Goncalves Narciso, Marcelo, 2002. "Using logical surrogate information in Lagrangean relaxation: An application to symmetric traveling salesman problems," European Journal of Operational Research, Elsevier, vol. 138(3), pages 473-483, May.
    3. Narciso, Marcelo G. & Lorena, Luiz Antonio N., 1999. "Lagrangean/surrogate relaxation for generalized assignment problems," European Journal of Operational Research, Elsevier, vol. 114(1), pages 165-177, April.
    4. Satoshi Suzuki & Daishi Kuroiwa, 2012. "Necessary and Sufficient Constraint Qualification for Surrogate Duality," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 366-377, February.
    5. R. Christopher L. Riley & Cesar Rego, 2019. "Intensification, diversification, and learning via relaxation adaptive memory programming: a case study on resource constrained project scheduling," Journal of Heuristics, Springer, vol. 25(4), pages 793-807, October.
    6. Khosla, Inder, 1995. "The scheduling problem where multiple machines compete for a common local buffer," European Journal of Operational Research, Elsevier, vol. 84(2), pages 330-342, July.
    7. Alidaee, Bahram, 2014. "Zero duality gap in surrogate constraint optimization: A concise review of models," European Journal of Operational Research, Elsevier, vol. 232(2), pages 241-248.
    8. Edirisinghe, Chanaka & Jeong, Jaehwan, 2019. "Indefinite multi-constrained separable quadratic optimization: Large-scale efficient solution," European Journal of Operational Research, Elsevier, vol. 278(1), pages 49-63.
    9. Renaud Chicoisne, 2023. "Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes," Computational Optimization and Applications, Springer, vol. 84(3), pages 789-831, April.
    10. Selcuk Karabati & Panagiotis Kouvelis & Gang Yu, 2001. "A Min-Max-Sum Resource Allocation Problem and Its Applications," Operations Research, INFORMS, vol. 49(6), pages 913-922, December.
    11. Ablanedo-Rosas, José H. & Rego, César, 2010. "Surrogate constraint normalization for the set covering problem," European Journal of Operational Research, Elsevier, vol. 205(3), pages 540-551, September.
    12. Suzuki, Satoshi & Kuroiwa, Daishi & Lee, Gue Myung, 2013. "Surrogate duality for robust optimization," European Journal of Operational Research, Elsevier, vol. 231(2), pages 257-262.
    13. Galvao, Roberto D. & Gonzalo Acosta Espejo, Luis & Boffey, Brian, 2000. "A comparison of Lagrangean and surrogate relaxations for the maximal covering location problem," European Journal of Operational Research, Elsevier, vol. 124(2), pages 377-389, July.
    14. Patriksson, Michael, 2008. "A survey on the continuous nonlinear resource allocation problem," European Journal of Operational Research, Elsevier, vol. 185(1), pages 1-46, February.
    15. Nieuwenhuizen, Thorsten, 1999. "Johri's general dual, the Lagrangian dual, and the surrogate dual," European Journal of Operational Research, Elsevier, vol. 117(1), pages 183-196, August.
    16. Satoshi Suzuki & Daishi Kuroiwa, 2020. "Duality Theorems for Convex and Quasiconvex Set Functions," SN Operations Research Forum, Springer, vol. 1(1), pages 1-13, March.
    17. N. Boland & A. C. Eberhard & A. Tsoukalas, 2015. "A Trust Region Method for the Solution of the Surrogate Dual in Integer Programming," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 558-584, November.
    18. Johri, Pravin K., 1996. "Implied constraints and an alternate unified development of nonlinear programming theory," European Journal of Operational Research, Elsevier, vol. 88(3), pages 537-549, February.
    19. Marco Antonio Boschetti & Vittorio Maniezzo, 2022. "Matheuristics: using mathematics for heuristic design," 4OR, Springer, vol. 20(2), pages 173-208, June.
    20. Yoon, Yourim & Kim, Yong-Hyuk & Moon, Byung-Ro, 2012. "A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 366-376.
    21. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "The selection allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 707-725, September.

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