A global optimization approach for solving non-monotone variational inequality problems

Solving non-monotone equilibrium problems via a DIRECT-type approach

“…Remark 1 Theorem 2 is a generalization of Lemma 2.1 proved in [29], which provides an estimate of the Lipschitz constant of the gap function ϕ 0 for a VI with Lipschitz continuous operator. In fact, when (EP) reduces to a VI, the regularization parameter α = 0 and the set B = C, then the value of the Lipschitz constant given in Theorem 2 coincides with that given in [29,Lemma 2.1].…”

“…A partition based algorithm is characterized by the rules used to generate the subset of indices I * k , and by the strategies applied to further partition the subsets {C i : i ∈ I * k }. In [29], the authors consider non-monotone VIs and use a Branch and Bound method similar to the one described in [19] to tackle the considered global optimization problems.…”

“…This fact suggests to use global optimization approaches to solve non-monotone EPs. Global optimization techniques have been considered in the literature only for two special classes of EPs: linear complementarity problems [1,39] and VI problems (a branch and bound method was proposed in [29] and a meta-heuristic algorithm in [30]).…”

Improving the Solution of Variational Inequalities Based on the Optimization Approach

“…and Q( ) * x = 0, i.e., reduce the original problem (1) to problem (6). It is difficult for VE to find evaluation functions that could be calculated rather easily.…”

“…Function (10) was used to develop global methods possessing both linear [1, 2, 5] and superlinear [6] rate of convergence on a polyhedron. For sets W, in the general case, a linearized VE is reduced to optimization problem (6), (10),…”