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Characterization of Solution Sets of Quasiconvex Programs

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  • J.P. Penot

    (University of Pau)

Abstract

We examine to what extent one can provide characterizations of the sets of solutions to quasiconvex programs using adapted subdifferentials which generalize known characterizations in the convex case.

Suggested Citation

  • J.P. Penot, 2003. "Characterization of Solution Sets of Quasiconvex Programs," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 627-636, June.
    • Handle: RePEc:spr:joptap:v:117:y:2003:i:3:d:10.1023_a:1023905907248
    DOI: 10.1023/A:1023905907248
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    References listed on IDEAS

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    1. Zang, I. & Choo, E.U. & Avriel, M., 1977. "On functions whose stationary points are global minima," LIDAM Reprints CORE 308, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Satoshi Suzuki, 2019. "Optimality Conditions and Constraint Qualifications for Quasiconvex Programming," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 963-976, December.
    2. Elisa Mastrogiacomo & Emanuela Rosazza Gianin, 2015. "Portfolio Optimization with Quasiconvex Risk Measures," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 1042-1059, October.
    3. Satoshi Suzuki, 2021. "Karush–Kuhn–Tucker type optimality condition for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 79(1), pages 191-202, January.
    4. Jean-Paul Penot, 2015. "Projective dualities for quasiconvex problems," Journal of Global Optimization, Springer, vol. 62(3), pages 411-430, July.
    5. Arnaldo S. Brito & J. X. Cruz Neto & Jurandir O. Lopes & P. Roberto Oliveira, 2012. "Interior Proximal Algorithm for Quasiconvex Programming Problems and Variational Inequalities with Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 217-234, July.
    6. V. Jeyakumar & G. M. Lee & G. Li, 2015. "Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 407-435, February.
    7. A. Kabgani & F. Lara, 2023. "Semistrictly and neatly quasiconvex programming using lower global subdifferentials," Journal of Global Optimization, Springer, vol. 86(4), pages 845-865, August.
    8. J.P. Penot, 2003. "Lagrangian Approach to Quasiconvex Programing," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 637-647, June.
    9. Xiangkai Sun & Kok Lay Teo & Liping Tang, 2019. "Dual Approaches to Characterize Robust Optimal Solution Sets for a Class of Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 984-1000, September.
    10. Vsevolod I. Ivanov, 2013. "Optimality Conditions and Characterizations of the Solution Sets in Generalized Convex Problems and Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 65-84, July.
    11. Nader Kanzi & Majid Soleimani-damaneh, 2020. "Characterization of the weakly efficient solutions in nonsmooth quasiconvex multiobjective optimization," Journal of Global Optimization, Springer, vol. 77(3), pages 627-641, July.
    12. S. K. Mishra & B. B. Upadhyay & Le Thi Hoai An, 2014. "Lagrange Multiplier Characterizations of Solution Sets of Constrained Nonsmooth Pseudolinear Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 763-777, March.
    13. Vsevolod I. Ivanov, 2019. "Characterizations of Solution Sets of Differentiable Quasiconvex Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 181(1), pages 144-162, April.
    14. Satoshi Suzuki & Daishi Kuroiwa, 2015. "Characterizations of the solution set for quasiconvex programming in terms of Greenberg–Pierskalla subdifferential," Journal of Global Optimization, Springer, vol. 62(3), pages 431-441, July.
    15. N. T. H. Linh & J.-P. Penot, 2012. "Generalized Affine Functions and Generalized Differentials," Journal of Optimization Theory and Applications, Springer, vol. 154(2), pages 321-338, August.
    16. Khanh, Phan Quoc & Quyen, Ho Thuc & Yao, Jen-Chih, 2011. "Optimality conditions under relaxed quasiconvexity assumptions using star and adjusted subdifferentials," European Journal of Operational Research, Elsevier, vol. 212(2), pages 235-241, July.

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