Characterizations of weak sharp solutions for variational inequalities on Hadamard manifolds and applications
Luong Van Nguyen, Nguyen Thi Huyen Thu, Nguyen Thai An · Journal of Industrial and Management Optimization · 2023
In this paper, we first present several characterizations for the weak sharpness of the solution set of variational inequality problems on Hadamard manifolds. Some of these results answer an open question raised in [L. V. Nguyen, Optimization, 70 (2021) 1443-1458]. We then establish some abstract results on the finite termination property for sequences generated by some iterative methods under the weak sharpness or linear conditioning of solution sets. Finally, finite convergence results for sequences generated by the proximal point algorithm for solving pseudomonotone variational inequalities are presented. Examples are also given to illustrate our results.