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Linear semi-infinite programming theory: An updated survey

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  • Goberna, M. A.
  • Lopez, M. A.

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  • Goberna, M. A. & Lopez, M. A., 2002. "Linear semi-infinite programming theory: An updated survey," European Journal of Operational Research, Elsevier, vol. 143(2), pages 390-405, December.
    • Handle: RePEc:eee:ejores:v:143:y:2002:i:2:p:390-405
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    1. S. Zlobec, 2001. "Stability in Linear Programming Models: An Index Set Approach," Annals of Operations Research, Springer, vol. 101(1), pages 363-382, January.
    2. M.J. Cánovas & M.A. López & J. Parra & M.I. Todorov, 2001. "Solving Strategies and Well-Posedness in Linear Semi-Infinite Programming," Annals of Operations Research, Springer, vol. 101(1), pages 171-190, January.
    3. Teresa León & Susana Sanmatías & Enriqueta Vercher, 1998. "A multi-local optimization algorithm," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 6(1), pages 1-18, June.
    4. Edward J. Anderson & Miguel A. Goberna & Marco A. López, 2001. "Simplex-Like Trajectories on Quasi-Polyhedral Sets," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 147-162, February.
    5. Francisco Guerra & Miguel Jiménez, 1998. "On feasible sets defined through Chebyshev approximation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 47(2), pages 255-264, June.
    6. A. Charnes & W. W. Cooper & K. Kortanek, 1963. "Duality in Semi-Infinite Programs and Some Works of Haar and Carathéodory," Management Science, INFORMS, vol. 9(2), pages 209-228, January.
    7. M. Gugat, 1999. "Convex Semi-Infinite Parametric Programming: Uniform Convergence of the Optimal Value Functions of Discretized Problems," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 191-201, April.
    8. M. A. Goberna & V. Jornet & R. Puente & M. I. Todorov, 1999. "Analytical Linear Inequality Systems and Optimization," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 95-119, October.
    9. Leon, T. & Sanmatias, S. & Vercher, E., 2000. "On the numerical treatment of linearly constrained semi-infinite optimization problems," European Journal of Operational Research, Elsevier, vol. 121(1), pages 78-91, February.
    10. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
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    Cited by:

    1. Mohammad R. Oskoorouchi & Hamid R. Ghaffari & Tamás Terlaky & Dionne M. Aleman, 2011. "An Interior Point Constraint Generation Algorithm for Semi-Infinite Optimization with Health-Care Application," Operations Research, INFORMS, vol. 59(5), pages 1184-1197, October.
    2. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    3. Balendu Bhooshan Upadhyay & Arnav Ghosh & Savin Treanţă, 2024. "Efficiency conditions and duality for multiobjective semi-infinite programming problems on Hadamard manifolds," Journal of Global Optimization, Springer, vol. 89(3), pages 723-744, July.
    4. Jeyakumar, V. & Li, G., 2010. "New strong duality results for convex programs with separable constraints," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1203-1209, December.
    5. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "An inexact primal-dual algorithm for semi-infinite programming," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(3), pages 501-544, June.
    6. S. Rivaz & M. A. Yaghoobi & M. Hladík, 2016. "Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 237-253, September.
    7. Nazih Abderrazzak Gadhi, 2019. "Necessary optimality conditions for a nonsmooth semi-infinite programming problem," Journal of Global Optimization, Springer, vol. 74(1), pages 161-168, May.
    8. He, Li & Huang, Guo H. & Lu, Hongwei, 2011. "Bivariate interval semi-infinite programming with an application to environmental decision-making analysis," European Journal of Operational Research, Elsevier, vol. 211(3), pages 452-465, June.
    9. S. Mishra & M. Jaiswal & H. Le Thi, 2012. "Nonsmooth semi-infinite programming problem using Limiting subdifferentials," Journal of Global Optimization, Springer, vol. 53(2), pages 285-296, June.
    10. Zhu, Y. & Huang, G.H. & Li, Y.P. & He, L. & Zhang, X.X., 2011. "An interval full-infinite mixed-integer programming method for planning municipal energy systems - A case study of Beijing," Applied Energy, Elsevier, vol. 88(8), pages 2846-2862, August.
    11. Amitabh Basu & Kipp Martin & Christopher Thomas Ryan, 2015. "Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 40(1), pages 146-170, February.
    12. Archis Ghate & Dushyant Sharma & Robert L. Smith, 2010. "A Shadow Simplex Method for Infinite Linear Programs," Operations Research, INFORMS, vol. 58(4-part-1), pages 865-877, August.
    13. Hassan Bakhtiari & Hossein Mohebi, 2021. "Lagrange Multiplier Characterizations of Constrained Best Approximation with Infinite Constraints," Journal of Optimization Theory and Applications, Springer, vol. 189(3), pages 814-835, June.
    14. P. Guo & G. Huang & L. He & H. Zhu, 2009. "Interval-parameter Two-stage Stochastic Semi-infinite Programming: Application to Water Resources Management under Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 23(5), pages 1001-1023, March.

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