Optimization Letters

, Volume 12, Issue 3, pp 519–534 | Cite as

Exact characterization for subdifferentials of a special optimal value function

Original Paper


For a closed set S and a bounded closed convex set U in a real normed vector space, we give exact subdifferential formulas of an optimal value function \(\mathrm {I}\!\Gamma _{S|U}\) whose definition is based on the Minkowski function of U. \(\mathrm {I}\!\Gamma _{S|U}\) covers distance function and indicator function as special cases. The main contribution is dropping two important assumptions of some main results in the literature.


Subdifferential Normal cone Optimal value function 



This work is supported by National Natural Science Foundation of China (Grant Nos. 11271274, 11461058), Scientific Research Fund of Sichuan Provincial Education Department (Grant Nos. 11ZB153, 11ZA180) and Scientific Research Fund of Sichuan Minzu College(Grant Nos. 13XYZB011, 12XYZB006).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsSichuan Normal UniversityChengduChina
  2. 2.Department of MathematicsSichuan Minzu CollegeKangdingChina

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