Two Optimal Value Functions in Parametric Conic Linear Programming

• Published in: Journal of optimization theory and applications Vol. 193; no. 1-3; pp. 574 - 597
• Main Authors: Luan, Nguyen Ngoc, Kim, Do Sang, Yen, Nguyen Dong
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Engineering; Euclidean geometry; Euclidean space; Feasibility; Linear programming; Mathematical analysis; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Perturbation; Theory of Computation; Conic linear programming; 90C31; Dual problem; Optimal value function; 90C30; 49K40; 90C25; Primal problem; Increment estimates; Lipschitz continuity; Differentiability properties
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-021-01959-z

We consider the conic linear program given by a closed convex cone in an Euclidean space and a matrix, where vector on the right-hand side of the inequality constraint and the vector defining the objective function are subject to change. Using the strict feasibility condition, we prove the locally Lipschitz continuity and obtain some differentiability properties of the optimal value function of the problem under right-hand-side perturbations. For the optimal value function under linear perturbations of the objective function, similar differentiability properties are obtained under the assumption saying that both primal problem and dual problem are strictly feasible.