Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

• Published in: Journal of optimization theory and applications Vol. 176; no. 1; pp. 205 - 224
• Main Author: Antczak, T.
• Format: Journal Article
• Language: English
• Published: New York Springer US 2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Engineering; Mathematical programming; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Penalty function; Queuing theory; Theory of Computation; Exact absolute value penalty function method; 49M30; 90C30; 90C25; Interval-valued optimization problem; Exactness of the exact absolute value penalty function method; Penalized optimization problem with the interval-valued exact absolute value penalty function; LU-convex function
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-017-1204-2

In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.