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Two Optimal Value Functions in Parametric Conic Linear Programming

Author

Listed:
  • Nguyen Ngoc Luan

    (Hanoi National University of Education)

  • Do Sang Kim

    (Pukyong National University)

  • Nguyen Dong Yen

    (Vietnam Academy of Science and Technology)

Abstract

We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the inequality constraint and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.

Suggested Citation

  • Nguyen Ngoc Luan & Do Sang Kim & Nguyen Dong Yen, 2022. "Two Optimal Value Functions in Parametric Conic Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 574-597, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01959-z
    DOI: 10.1007/s10957-021-01959-z
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    References listed on IDEAS

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    5. E. A. Yildirim, 2004. "Unifying Optimal Partition Approach to Sensitivity Analysis in Conic Optimization," Journal of Optimization Theory and Applications, Springer, vol. 122(2), pages 405-423, August.
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