Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas

Duong Thi Viet An (1, 2) , Abderrahim Jourani (3)

1 HDU - Hangzhou Dianzi University
2 Department of Mathematics, Thai Nguyen University of Education
3 IMB - Institut de Mathématiques de Bourgogne [Dijon]

The aim of the present work is to use a metric intersection formula to estimate the subdifferential of the marginal function in the convex setting. This intersection formula includes many interesting situations in parametric convex programming, including the polyhedral one. It is expressed in terms of the objective function and the constrained multivalued mapping which govern the parametric program.

Mots clés: Parametric convex programming; marginal function; subdifferential; singular subdifferential; distance function

Domaines: Optimisation et contrôle [math.OC]

Duong Thi Viet An, Abderrahim Jourani. Subdifferentials of the Marginal Functions in Parametric Convex Optimization via Intersection Formulas. Journal of Optimization Theory and Applications, 2022, 192 (1), pp.82-96. ⟨10.1007/s10957-021-01952-6⟩. ⟨hal-03448368⟩