Thanh Quoc Trinh | Searcharxiv

arXiv2026

The Popov's Algorithm with Optimal Bounded Stepsize for Generalized Monotone Variational Inequalities

For solving unconstrained generalized monotone variational inequality, we prove that the iterations generated by Popov algorithm converge to a solution when stepsize is smaller than $\frac{1}{\sqrt{3}L}$, where $L$ is the Lipschitz constant of the variational inequality operator. The convergence analysis is carried out by using a new Lyapunov-type function. In addition, we prove that the upper bound $\frac{1}{\sqrt{3}L}$ is tight. Finally, we extend the results to variational inequality with linear subspace constraints.

math.OC↗

arXiv2026

Second order continuous and discrete dynamical systems for solving inverse quasi-variational inequalities

In this paper, we investigate the inverse quasi-variational inequality problem in finite-dimensional spaces. First, we introduce a second-order dynamical system whose trajectory converges exponentially to the solution of the inverse quasi-variational inequality, under the assumptions of Lipschitz continuity and strong monotonicity. Next, we discretize the proposed dynamical system to develop an algorithm, and prove that the iterations converge linearly to the unique solution of the inverse quasi-variational inequality. Finally, we present numerical experiments and applications to validate the theoretical results and compare the performance with existing methods.

math.OC↗