This paper proposes an accelerated proximal point method for maximally monotone operators. The proof is computer-assisted via the performance estimation problem approach. includes various well-known convex optimization methods, such as of multipliers and alternating direction multipliers, thus proposed acceleration has wide applications. Numerical experiments are presented to demonstrate accele...

The viscosity solution of static Hamilton-Jacobi equations with a pointsource condition has an upwind singularity at the source, which makes all formally high-order finite-difference scheme exhibit first-order convergence and relatively large errors. To obtain designed high-order accuracy, one needs to treat this source singularity during computation. In this paper, we apply the factorization i...

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem’s data, the method is proved to converges globally. Some preliminary computational results are also r...

In this paper we present a subgradient method with non-monotone line search for the minimization of convex functions simple constraints. Different from standard prefixed step sizes, new selects sizes in an adaptive way. Under mild conditions asymptotic convergence results and iteration-complexity bounds are obtained. Preliminary numerical illustrate relative efficiency proposed method.

We propose a sequential method to estimate monotone convex function that consists of: (i) monotone regression via solving a constrained least square problem and (ii) convexification of the monotone regression estimate via solving an associated constrained uniform approximation problem. We show that this method is faster than the constrained least squares (LS) method. The ratio of computation ti...

We propose a descent method via gap functions for solving nonsmooth variational inequalities with a locally Lipschitz operator. Assuming monotone operator (not necessarily strongly monotone) and bounded domain, we show that the method with an Armijo-type line search is globally convergent. Finally, we report some numerical experiments.