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We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
In this paper we consider a class of monotone inclusion (MI) problems of finding a zero of the sum of two monotone operators, in which one operator is maximal monotone while the other is {\it locally Lipschitz} continuous. We propose…
The aim of this paper is to present an extragradient method for variational inequality associated to a point-to-set vector field in Hadamard manifolds and to study its convergence properties. In order to present our method the concept of…
In this work, we present new simple and optimal algorithms for solving the variational inequality (VI) problem for $p^{th}$-order smooth, monotone operators -- a problem that generalizes convex optimization and saddle-point problems. Recent…
In this paper, we propose new algorithms for finding a common point of the solution set of a pseudomonotone equilibrium problem and the set of fixed points of a symmetric generalized hybrid mapping in a real Hilbert space. The convergence…
The paper presents a fully explicit algorithm for monotone variational inequalities. The method uses variable stepsizes that are computed using two previous iterates as an approximation of the local Lipschitz constant without running a…
This paper is a survey of methods for solving smooth (strongly) monotone stochastic variational inequalities. To begin with, we give the deterministic foundation from which the stochastic methods eventually evolved. Then we review methods…
Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…
We propose in this work a subgradient extragradient method with inertial and correction terms for solving equilibrium problems in a real Hilbert space. We obtain that the sequence generated by our proposed method converges weakly to a point…
This paper proposes an extra gradient Anderson-accelerated algorithm for solving pseudomonotone variational inequalities, which uses the extra gradient scheme with line search to guarantee the global convergence and Anderson acceleration to…
We present and study the iteration-complexity of a relative-error inexact proximal-Newton extragradient algorithm for solving smooth monotone variational inequality problems in real Hilbert spaces. We removed a search procedure from…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
In this paper, we study both elliptic and parabolic equations in non-divergence form with singular degenerate coefficients. Weighted and mixed-norm $L_p$-estimates and solvability are established under some suitable partially weighted BMO…
This paper considers the problems of solving monotone variational inequalities with H\"older continuous Jacobians. By employing the knowledge of H\"older parameter $\nu$, we propose the $\nu$-regularized extra-Newton method within at most…
The subgradient method is one of the most fundamental algorithmic schemes for nonsmooth optimization. The existing complexity and convergence results for this method are mainly derived for Lipschitz continuous objective functions. In this…
This paper establishes comprehensive stability results for quasi-variational inequalities (QVIs) under monotone perturbations of the governing operator. We prove strong convergence of both minimal and maximal solutions when sequences of…
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also…
This paper is concerned with nonlinear elliptic equations in nondivergence form where the operator has a first order drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative…
Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged and nonexpansive operators. The structure and properties of the compositions are of…
In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by the sum of a possibly nonsmooth nonconvex function and a differentiable function whose gradient is…