Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

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

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 1, No 6, 126-143

Abstract: Abstract This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for $$\varepsilon $$ ε -subdifferentials, we obtain exact formulas for computing the $$\varepsilon $$ ε -subdifferential of the optimal value function. Several illustrative examples are also given.

Keywords: Parametric convex programming; Optimal value function; Conjugate function; $$\varepsilon $$ ε -Subdifferentials; $$\varepsilon $$ ε -Normal directions; 49J53; 49Q12; 90C25; 90C31 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1431-1

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