Nonsmooth variational-like inequalities and nonsmooth vector optimization |
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| Authors: | M. Alshahrani Q. H. Ansari S. Al-Homidan |
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| Affiliation: | 1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
2. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India
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| Abstract: | In this paper, we consider nonsmooth vector variational-like inequalities and nonsmooth vector optimization problems. By using the scalarization method, we define nonsmooth variational-like inequalities by means of Clarke generalized directional derivative and study their relations with the vector optimizations and the scalarized optimization problems. Some existence results for solutions of our nonsmooth variational-like inequalities are presented under densely pseudomonotonicity or pseudomonotonicity assumption. |
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