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Strong duality for standard convex programs

Author

Listed:
  • Kenneth O. Kortanek

    (University of Pittsburgh)

  • Guolin Yu

    (North Minzu University)

  • Qinghong Zhang

    (Northern Michigan University)

Abstract

A primal optimization problem and its dual are in strong duality if either one of the problems has a finite optimal value, then the other one is consistent and has the same optimal value, and the optimal value of the dual problem is attained. In this paper, we study the strong duality without constraint qualifications for a standard convex optimization problem using the bifunction, image space analysis, and polynomial ring approaches. We obtain new strong duals for the primal convex optimization problem, which to the best of our knowledge have not been appeared in the related literature.

Suggested Citation

  • Kenneth O. Kortanek & Guolin Yu & Qinghong Zhang, 2021. "Strong duality for standard convex programs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(3), pages 413-436, December.
    • Handle: RePEc:spr:mathme:v:94:y:2021:i:3:d:10.1007_s00186-021-00761-x
    DOI: 10.1007/s00186-021-00761-x
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    References listed on IDEAS

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    1. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    2. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part II: Duality and Penalization," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 637-659, June.
    3. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part III: Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 660-678, June.
    4. 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.
    5. Luo, Z-Q. & Sturm, J.F. & Zhang, S., 1997. "Duality Results for Conic Convex Programming," Econometric Institute Research Papers EI 9719/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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