We introduce a new approximation scheme combining the viscosity method with extragradient method for finding a common element of the set of solutions of a mixed equilibrium problem and the set of fixed points of a finite family of nonexpansive mappings and the set of the variational inequality for a monotone, Lipschitz continuous mapping. We obtain a strong convergence theorem for the sequences...

In this paper, we study the strong convergence of two Mann-type inertial extragradient algorithms, which are devised with a new step size, for solving variational inequality problem monotone and Lipschitz continuous operator in real Hilbert spaces. Strong theorems our algorithms proved without prior knowledge constant operator. Finally, provide some numerical experiments to illustrate performan...

We present a simple and scalable algorithm for maximum-margin estimation of structured output models, including an important class of Markov networks and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem that allows us to use simple projection methods based on the dual extragradient algorithm (Nesterov, 2003). The projection step can be solved us...

We present a simple and scalable algorithm for large-margin estimation of structured models, including an important class of Markov networks and combinatorial models. The estimation problem can be formulated as a quadratic program (QP) that exploits the problem structure to achieve polynomial number of variables and constraints. However, off-the-shelf QP solvers scale poorly with problem and tr...

Stability has been a recurrent issue in training generative adversarial networks (GANs). One common way to tackle this issue has been to propose new formulations of the GAN objective. Yet, surprisingly few studies have looked at optimization methods specifically designed for this adversarial training. In this work, we review the “variational inequality” framework which contains most formulation...

We introduce a new hybrid extragradient viscosity approximationmethod for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed i...

* Correspondence: [email protected] Department of Applied Mathematics, Chung Yuan Christian University, Chung Li 32023, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we suggest a hybrid method for finding a common element of the set of solution of a monotone, Lipschitz-continuous variational inequality problem and the set of common fixed ...

In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general nonconvex quasi variational inequalities and the fixed point problems. This alternative equivalent formul...

IVIM MR imaging is a method which generates images of diffusion and perfusion in vivo. Until now, intravoxel incoherent motion (IVIM) images have been obtained using spin-echo sequences with extragradient pulses, resulting in long acquisition times (typically 2 x 8 min 32 s). A new method is proposed here, using steady-state free precession (SSFP), which allows IVIM images to be obtained in a c...