A NEW NON-LIPSCHITZIAN PROJECTION METHOD FOR SOLVING VARIATIONAL INEQUALITIES IN EUCLIDEAN SPACES - Gibali, A. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2015)
The extragradient method introduced by Korpelevich [18] and Antipin [1] is a double projection method designed for solving variational inequalities. The double projection per iteration enable to obtain convergent under monotonicity and Lipschitz continuity while other single projection methods, for example the projected gradient method requires strong monotonicity. The subgradient extragradient method [5] is a modification of the extragradient in which the second projection onto the feasible set is replaced by a projection onto a specific constructible half-space which is actually one of the subgradient half-spaces. Still, this algorithm requires Lipschitz continuity. In this work we introduce a self-adaptive subgradient extragradient method by adopting Armijo-like searches which enables to obtain convergent under the assumption of pseudo-monotonicity and continuity.