Paper Title:

New Fast Extragradient-like Methods for Non-Lipschitzian Pseudo-monotone Variational Inequalities

Author(s):

Morad Ali Peyvand

Department of Mathematics
Yasouj University
Yasouj,
Iran.
E-mail: peyvand@yu.ac.ir

Abstract:

An efficient double-projection method, with a new search strategy, is designed for solving variational inequalities in real Hilbert spaces with pseudo-monotone cost operator. Our proposed method uses a computationally inexpensive simple line search procedure based on local information of the operator and very weak conditions of parameters to obtain larger step sizes. A description of the algorithm along with its weak convergence is provided without assuming Lipschitz continuity. Also, a modification to the proposed method is presented, wherein the second projection onto the closed and convex subset is replaced with the one onto a subgradient half space. Numerical experiments and comparisons with related methods demonstrate the reliability and benefits of the proposed schemes.

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