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On generalized semi-infinite optimization and bilevel optimization

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  • Stein, Oliver
  • Still, Georg

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  • Stein, Oliver & Still, Georg, 2002. "On generalized semi-infinite optimization and bilevel optimization," European Journal of Operational Research, Elsevier, vol. 142(3), pages 444-462, November.
    • Handle: RePEc:eee:ejores:v:142:y:2002:i:3:p:444-462
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    References listed on IDEAS

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    1. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
    2. Jan-J. Rückmann & Oliver Stein, 2001. "On Linear and Linearized Generalized Semi-Infinite Optimization Problems," Annals of Operations Research, Springer, vol. 101(1), pages 191-208, January.
    3. G. Stein & G. Still, 2000. "On Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 443-458, February.
    4. J. J. Rückmann & A. Shapiro, 1999. "First-Order Optimality Conditions in Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 677-691, June.
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    Citations

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    Cited by:

    1. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    2. Alexander Mitsos & Angelos Tsoukalas, 2015. "Global optimization of generalized semi-infinite programs via restriction of the right hand side," Journal of Global Optimization, Springer, vol. 61(1), pages 1-17, January.
    3. Peter Kirst & Oliver Stein, 2016. "Solving Disjunctive Optimization Problems by Generalized Semi-infinite Optimization Techniques," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 1079-1109, June.
    4. Stein, Oliver, 2012. "How to solve a semi-infinite optimization problem," European Journal of Operational Research, Elsevier, vol. 223(2), pages 312-320.
    5. R. Paulavičius & C. S. Adjiman, 2020. "New bounding schemes and algorithmic options for the Branch-and-Sandwich algorithm," Journal of Global Optimization, Springer, vol. 77(2), pages 197-225, June.
    6. Hatim Djelassi & Moll Glass & Alexander Mitsos, 2019. "Discretization-based algorithms for generalized semi-infinite and bilevel programs with coupling equality constraints," Journal of Global Optimization, Springer, vol. 75(2), pages 341-392, October.
    7. M. Beatrice Lignola & Jacqueline Morgan, 2017. "Inner Regularizations and Viscosity Solutions for Pessimistic Bilevel Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 183-202, April.
    8. L. J. Lin & H. J. Shie, 2008. "Existence Theorems of Quasivariational Inclusion Problems with Applications to Bilevel Problems and Mathematical Programs with Equilibrium Constraint," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 445-457, September.
    9. Vandana Goyal & Namrata Rani & Deepak Gupta, 2021. "Parametric approach to quadratically constrained multi-level multi-objective quadratic fractional programming," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 557-574, September.
    10. Hirotaka Takano & Ryosuke Hayashi & Hiroshi Asano & Tadahiro Goda, 2021. "Optimal Sizing of Battery Energy Storage Systems Considering Cooperative Operation with Microgrid Components," Energies, MDPI, vol. 14(21), pages 1-13, November.
    11. Volker Maag, 2015. "A collision detection approach for maximizing the material utilization," Computational Optimization and Applications, Springer, vol. 61(3), pages 761-781, July.
    12. Hatim Djelassi & Alexander Mitsos, 2017. "A hybrid discretization algorithm with guaranteed feasibility for the global solution of semi-infinite programs," Journal of Global Optimization, Springer, vol. 68(2), pages 227-253, June.
    13. L. J. Lin, 2008. "Existence Theorems for Bilevel Problem with Applications to Mathematical Program with Equilibrium Constraint and Semi-Infinite Problem," Journal of Optimization Theory and Applications, Springer, vol. 137(1), pages 27-40, April.
    14. Polyxeni-Margarita Kleniati & Claire Adjiman, 2014. "Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development," Journal of Global Optimization, Springer, vol. 60(3), pages 425-458, November.
    15. J. J. Ye & S. Y. Wu, 2008. "First Order Optimality Conditions for Generalized Semi-Infinite Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 419-434, May.
    16. Geletu, Abebe & Hoffmann, Armin, 2004. "A conceptual method for solving generalized semi-infinite programming problems via global optimization by exact discontinuous penalization," European Journal of Operational Research, Elsevier, vol. 157(1), pages 3-15, August.
    17. 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.
    18. Dajun Yue & Jiyao Gao & Bo Zeng & Fengqi You, 2019. "A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs," Journal of Global Optimization, Springer, vol. 73(1), pages 27-57, January.
    19. S. Dempe & S. Franke, 2016. "On the solution of convex bilevel optimization problems," Computational Optimization and Applications, Springer, vol. 63(3), pages 685-703, April.
    20. T. Q. Son & J. J. Strodiot & V. H. Nguyen, 2009. "ε-Optimality and ε-Lagrangian Duality for a Nonconvex Programming Problem with an Infinite Number of Constraints," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 389-409, May.
    21. 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.
    22. Oliver Stein, 2012. "Comments on: Stability in linear optimization and related topics. A personal tour," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 265-266, July.
    23. Wang, Guangmin & Gao, Ziyou & Xu, Meng & Sun, Huijun, 2014. "Joint link-based credit charging and road capacity improvement in continuous network design problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 67(C), pages 1-14.
    24. O. Stein & A. Winterfeld, 2010. "Feasible Method for Generalized Semi-Infinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 419-443, August.

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