Differential Stability of Convex Optimization Problems with Possibly Empty Solution Sets

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

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 181; no. 1; pp. 126 - 143
Main Authors: An, Duong Thi Viet, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: New York Springer US 01.04.2019
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Computational geometry
Convex analysis
Convexity
Dimensional stability
Engineering
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Sum rules
Theory of Computation
90C31
Optimal value function
Subdifferentials
49J53
90C25
Conjugate function
Parametric convex programming
49Q12
Normal directions
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper studies differential stability of infinite-dimensional convex optimization problems, whose solution sets may be empty. By using suitable sum rules for ε -subdifferentials, we obtain exact formulas for computing the ε -subdifferential of the optimal value function. Several illustrative examples are also given.
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content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-018-1431-1