The KKT optimality conditions for optimization problem with interval-valued objective function on Hadamard manifolds.
- Resource Type
- Article
- Authors
- Chen, Sheng-lan
- Source
- Optimization. Mar2022, Vol. 71 Issue 3, p613-632. 20p.
- Subject
- *SET-valued maps
*PROBLEM solving
*CONVEX functions
- Language
- ISSN
- 0233-1934
In this paper, we study the Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function on Hadamard manifolds. The gH-directional differentiability for interval-valued function is defined by using the generalized Hukuhara difference. The concepts of interval-valued convexity and pseudoconvexity are introduced on Hadamard manifolds, and several properties involving such functions are also given. Under these settings, we derive the KKT optimality conditions and give a numerical example to show that the results obtained in this paper are more general than the corresponding conclusions of Wu [The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur J Oper Res. 2007;176:46–59] in solving the optimization problem with interval-valued objective function. [ABSTRACT FROM AUTHOR]