Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity
In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notion...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Belgrade
2017-01-01
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| Series: | Yugoslav Journal of Operations Research |
| Subjects: | |
| Online Access: | http://www.doiserbia.nb.rs/img/doi/0354-0243/2017/0354-02431700013U.pdf |
| Summary: | In this paper, we define some new generalizations of strongly convex
functions of order m for locally Lipschitz functions using Clarke
subdifferential. Suitable examples illustrating the non emptiness of the
newly defined classes of functions and their relationships with classical
notions of pseudoconvexity and quasiconvexity are provided. These
generalizations are then employed to establish sufficient optimality
conditions for a nonsmooth multiobjective optimization problem involving
support functions of compact convex sets. Furthermore, we formulate a mixed
type dual model for the primal problem and establish weak and strong duality
theorems using the notion of strict efficiency of order m. The results
presented in this paper extend and unify several known results from the
literature to a more general class of functions as well as optimization
problems. |
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| ISSN: | 0354-0243 1820-743X |