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How to solve a semi-infinite optimization problem

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  • Stein, Oliver
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    Abstract

    After an introduction to main ideas of semi-infinite optimization, this article surveys recent developments in theory and numerical methods for standard and generalized semi-infinite optimization problems. Particular attention is paid to connections with mathematical programs with complementarity constraints, lower level Wolfe duality, semi-smooth approaches, as well as branch and bound techniques in adaptive convexification procedures. A section on recent genericity results includes a discussion of the symmetry effect in generalized semi-infinite optimization.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 2 ()
    Pages: 312-320

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:312-320

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    Web page: http://www.elsevier.com/locate/eor

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    Keywords: Semi-infinite optimization; Design centering; Robust optimization; Adaptive convexification; Genericity;

    References

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    1. Harald G├╝nzel & Hubertus Jongen & Oliver Stein, 2007. "On the closure of the feasible set in generalized semi-infinite programming," Central European Journal of Operations Research, Springer, vol. 15(3), pages 271-280, September.
    2. Still, G., 1999. "Generalized semi-infinite programming: Theory and methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 301-313, December.
    3. Winterfeld, Anton, 2008. "Application of general semi-infinite programming to lapidary cutting problems," European Journal of Operational Research, Elsevier, vol. 191(3), pages 838-854, December.
    4. Kanzi, N. & Nobakhtian, S., 2010. "Necessary optimality conditions for nonsmooth generalized semi-infinite programming problems," European Journal of Operational Research, Elsevier, vol. 205(2), pages 253-261, September.
    5. Ralf Werner, 2008. "Cascading: an adjusted exchange method for robust conic programming," Central European Journal of Operations Research, Springer, vol. 16(2), pages 179-189, June.
    6. Lopez, Marco & Still, Georg, 2007. "Semi-infinite programming," European Journal of Operational Research, Elsevier, vol. 180(2), pages 491-518, July.
    7. 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.
    8. Gerhard-Wilhelm Weber & Aysun Tezel, 2007. "On generalized semi-infinite optimization of genetic networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 15(1), pages 65-77, July.
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    Cited by:
    1. Soleimanian, Azam & Salmani Jajaei, Ghasemali, 2013. "Robust nonlinear optimization with conic representable uncertainty set," European Journal of Operational Research, Elsevier, vol. 228(2), pages 337-344.
    2. M. Diehl & B. Houska & O. Stein & P. Steuermann, 2013. "A lifting method for generalized semi-infinite programs based on lower level Wolfe duality," Computational Optimization and Applications, Springer, vol. 54(1), pages 189-210, January.
    3. Oliver Stein & Nathan Sudermann-Merx, 2014. "On smoothness properties of optimal value functions at the boundary of their domain under complete convexity," Mathematical Methods of Operations Research, Springer, vol. 79(3), pages 327-352, June.

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