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Nonlinear Optimization by Successive Linear Programming

Author

Listed:
  • F. Palacios-Gomez

    (Universidad Distrital de Bogota, Bogota, Colombia)

  • L. Lasdon

    (University of Texas at Austin)

  • M. Engquist

    (University of Texas at Austin)

Abstract

Successive Linear Programming (SLP), which is also known as the Method of Approximation Programming, solves nonlinear optimization problems via a sequence of linear programs. This paper reports on promising computational results with SLP that contrast with the poor performance indicated by previously published comparative tests. The paper provides a detailed description of an efficient, reliable SLP algorithm along with a convergence theorem for linearly constrained problems and extensive computational results. It also discusses several alternative strategies for implementing SLP. The computational results show that SLP compares favorably with the Generalized Reduced Gradient Code GRG2 and with MINOS/GRG. It appears that SLP will be most successful when applied to large problems with low degrees of freedom.

Suggested Citation

  • F. Palacios-Gomez & L. Lasdon & M. Engquist, 1982. "Nonlinear Optimization by Successive Linear Programming," Management Science, INFORMS, vol. 28(10), pages 1106-1120, October.
    • Handle: RePEc:inm:ormnsc:v:28:y:1982:i:10:p:1106-1120
    DOI: 10.1287/mnsc.28.10.1106
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    Citations

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    Cited by:

    1. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    2. Les Foulds & Daniel Duarte & Hugo Nascimento & Humberto Longo & Bryon Hall, 2014. "Turning restriction design in traffic networks with a budget constraint," Journal of Global Optimization, Springer, vol. 60(2), pages 351-371, October.
    3. András Kovács, 2021. "Inverse optimization approach to the identification of electricity consumer models," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 521-537, June.
    4. Foulds, Les R. & do Nascimento, Hugo A.D. & Calixto, Iacer C.A.C. & Hall, Bryon R. & Longo, Humberto, 2013. "A fuzzy set-based approach to origin–destination matrix estimation in urban traffic networks with imprecise data," European Journal of Operational Research, Elsevier, vol. 231(1), pages 190-201.
    5. Mohammed Alfaki & Dag Haugland, 2014. "A cost minimization heuristic for the pooling problem," Annals of Operations Research, Springer, vol. 222(1), pages 73-87, November.
    6. Michelle L. Blom & Christina N. Burt & Adrian R. Pearce & Peter J. Stuckey, 2014. "A Decomposition-Based Heuristic for Collaborative Scheduling in a Network of Open-Pit Mines," INFORMS Journal on Computing, INFORMS, vol. 26(4), pages 658-676, November.
    7. Charles Audet & Jack Brimberg & Pierre Hansen & Sébastien Le Digabel & Nenad Mladenovi'{c}, 2004. "Pooling Problem: Alternate Formulations and Solution Methods," Management Science, INFORMS, vol. 50(6), pages 761-776, June.
    8. Cheng, Xianliang & Feng, Suzhen & Zheng, Hao & Wang, Jinwen & Liu, Shuangquan, 2022. "A hierarchical model in short-term hydro scheduling with unit commitment and head-dependency," Energy, Elsevier, vol. 251(C).
    9. Erfan Mohagheghi & Mansour Alramlawi & Aouss Gabash & Pu Li, 2018. "A Survey of Real-Time Optimal Power Flow," Energies, MDPI, vol. 11(11), pages 1-20, November.
    10. Daniel De Wolf & Yves Smeers, 2000. "The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm," Management Science, INFORMS, vol. 46(11), pages 1454-1465, November.
    11. L. F. Bueno & G. Haeser & J. M. Martínez, 2015. "A Flexible Inexact-Restoration Method for Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 165(1), pages 188-208, April.
    12. Zhongzheng He & Chao Wang & Yongqiang Wang & Hairong Zhang & Heng Yin, 2022. "An Efficient Optimization Method for Long-term Power Generation Scheduling of Hydropower Station: Improved Dynamic Programming with a Relaxation Strategy," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(4), pages 1481-1497, March.
    13. Hong, Sung-Pil & Kim, Taegyoon & Lee, Subin, 2019. "A precision pump schedule optimization for the water supply networks with small buffers," Omega, Elsevier, vol. 82(C), pages 24-37.
    14. Mohammed Alfaki & Dag Haugland, 2013. "Strong formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 897-916, July.
    15. Sarker, Ruhul A. & Gunn, Eldon A., 1997. "A simple SLP algorithm for solving a class of nonlinear programs," European Journal of Operational Research, Elsevier, vol. 101(1), pages 140-154, August.

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