Further Results on Differential Stability of Convex Optimization Problems

Duong Thi Viet An () and Jen-Chih Yao ()
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Duong Thi Viet An: Thai Nguyen University
Jen-Chih Yao: China Medical University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 2, 28-42

Abstract: Abstract As a complement to a recent paper by An and Yen (Appl Anal 94:108–128, 2015) on subdifferentials of the optimal value function in parametric convex programming under inclusion constraints and functional constraints, this paper studies the differential stability of convex optimization problems under a regularity condition of Aubin’s type (Aubin in Optima and equilibria: an introduction to nonlinear analysis. Springer, New York, 1998). By a suitable sum rule for convex subdifferentials, we obtain exact formulas for the subdifferential and singular subdifferential of the optimal value function. Illustrative examples and a detailed comparison of our results with those of the above-mentioned paper are given.

Keywords: Parametric convex programming; Optimal value function; Subdifferential; Singular subdifferential; Aubin’s regularity condition; 49J53; 49Q12; 90C25; 90C31 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-016-0900-7

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