Abstract
In this paper, we study the weak sharp solutions for nonsmooth variational inequalities and give a characterization in terms of error bound. Some characterizations of solution set of nonsmooth variational inequalities are presented. Under certain conditions, we prove that the sequence generated by an algorithm for finding a solution of nonsmooth variational inequalities terminates after a finite number of iterates provided that the solutions set of a nonsmooth variational inequality is weakly sharp. We also study the finite termination property of the gradient projection method for solving nonsmooth variational inequalities under weak sharpness of the solution set.
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Acknowledgements
In this research, the first and second author were funded by the National Plan for Science, Technology and Innovation (MAARIFAH) - King Abdulaziz City for Science and Technology - through the Science and Technology Unit at King Fahd University of Petroleum and Minerals (KFUPM) - the Kingdom of Saudi Arabia, award Number 12-MAT3023-24.
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Al-Homidan, S., Ansari, Q.H. & Van Nguyen, L. Weak Sharp Solutions for Nonsmooth Variational Inequalities. J Optim Theory Appl 175, 683–701 (2017). https://doi.org/10.1007/s10957-017-1181-5
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DOI: https://doi.org/10.1007/s10957-017-1181-5
Keywords
- Nonsmooth variational inequalities
- Weak sharp solutions
- Finite termination property
- Pseudomonotone operators