Abstract
ABSTRACT In this paper, we first present a modified double projection algorithm (MDPA for short) for solving variational inequality problems (VIP for short) without monotonicity. Compared with the algorithm of Ye and He [Comput Optim Appl. 2015;60(1):141–150], the next iterate point of MDPA is generated by projecting the current iterate point onto the intersection of the feasible set and only one half-space. Hence, MDPA can save the computational cost of computing the next iterate point. Moreover, we present a new MDPA (NMDPA for short) to decrease the total number of iterations of MDPA. The computational cost of NMDPA is the same as that of MDPA in each iteration. The global convergence of both MDPA and NMDPA is established under the same assumption that the underlying mapping is continuous and the solution set of its dual variational inequality is nonempty. Numerical experiments show that NMDPA can accelerate MDPA for solving nonmonotone VIP from the total number of iterative point of view and the CPU time point of view. Moreover, NMDPA is more efficient than Algorithm 1 of Dinh et al. [Numer Algorithms. 2022;90(4):1715–1734] from the CPU time point of view and the total number of iterations point of view.
Published Version
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