Henig proper subdifferential of set-valued maps
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We present a notion of Henig proper subdifferential and characterize it in terms of Henig efficiency. We also present existence and some calculus rules for Henig proper subdifferentials. Using this subdifferential, we derive optimality criteria for a constrained set-valued optimization problem.
KeywordsHenig proper subdifferential Proper efficiency Set-valued map Optimality conditions
Mathematics Subject Classification49K30 90C46
The author would like to express her sincere gratitude towards the anonymous referees for providing many helpful suggestions which enhanced the level of the paper. Also, the author would like to thank Prof. C.S. Lalitha, University of Delhi South Campus, New Delhi, India for providing her insight and expertise to this research work.
- 8.Jahn, J.: Vector Optimization. Theory, Applications, and Extensions, 2nd edn. Springer, Berlin (2011)Google Scholar
- 9.Kuhn, H.W., Tucker, A.W.: Nonlinear programming. In: Neyman, J. (ed.) Proceedings of Second Berkeley Symposium on Mathematical Statistics and Probability, pp. 481–492. University of California Press, Berkeley (1951)Google Scholar
- 13.Rockafellar, R.T.: Convex functions and dual extremum problems. Thesis Harvard, MA (1963)Google Scholar
- 14.Swaragi, Y., Nakayama, H., Tanino, T.: Theory of Multiobjective Optimization, Mathematics in Science and engineering, vol. 176. Academic Press, Orlando (1985)Google Scholar
- 18.Yu, G.: Generalized gradients in sense of Henig efficiency for set-valued maps. In: Proceedings of the 2009 International Joint Conference on Computational Sciences and Optimization. CSO 2009 (Volume 02), pp. 723–726 (2009)Google Scholar