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New strong duality results for convex programs with separable constraints

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  • Jeyakumar, V.
  • Li, G.

Abstract

It is known that convex programming problems with separable inequality constraints do not have duality gaps. However, strong duality may fail for these programs because the dual programs may not attain their maximum. In this paper, we establish conditions characterizing strong duality for convex programs with separable constraints. We also obtain a sub-differential formula characterizing strong duality for convex programs with separable constraints whenever the primal problems attain their minimum. Examples are given to illustrate our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:207:y:2010:i:3:p:1203-1209
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    References listed on IDEAS

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    1. 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.
    2. V. Jeyakumar, 2008. "Constraint Qualifications Characterizing Lagrangian Duality in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 31-41, January.
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    Cited by:

    1. T. D. Chuong & V. H. Mak-Hau & J. Yearwood & R. Dazeley & M.-T. Nguyen & T. Cao, 2022. "Robust Pareto solutions for convex quadratic multiobjective optimization problems under data uncertainty," Annals of Operations Research, Springer, vol. 319(2), pages 1533-1564, December.
    2. V. Jeyakumar & J. Vicente-Pérez, 2014. "Dual Semidefinite Programs Without Duality Gaps for a Class of Convex Minimax Programs," Journal of Optimization Theory and Applications, Springer, vol. 162(3), pages 735-753, September.
    3. Nguyen Minh Tung & Mai Duy, 2023. "Constraint qualifications and optimality conditions for robust nonsmooth semi-infinite multiobjective optimization problems," 4OR, Springer, vol. 21(1), pages 151-176, March.
    4. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2020. "A Unified Approach Through Image Space Analysis to Robustness in Uncertain Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 466-493, February.
    5. Jae Hyoung Lee & Gue Myung Lee, 2018. "On optimality conditions and duality theorems for robust semi-infinite multiobjective optimization problems," Annals of Operations Research, Springer, vol. 269(1), pages 419-438, October.
    6. T. D. Chuong & V. Jeyakumar & G. Li & D. Woolnough, 2021. "Exact SDP reformulations of adjustable robust linear programs with box uncertainties under separable quadratic decision rules via SOS representations of non-negativity," Journal of Global Optimization, Springer, vol. 81(4), pages 1095-1117, December.
    7. V. Jeyakumar & G. Y. Li, 2011. "Robust Duality for Fractional Programming Problems with Constraint-Wise Data Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 151(2), pages 292-303, November.
    8. Satoshi Suzuki & Daishi Kuroiwa, 2017. "Duality Theorems for Separable Convex Programming Without Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 172(2), pages 669-683, February.

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