Related papers: Extragradient and linesearch algorithms for solvin…
In this paper, we use a Banach fixed point theorem to obtain suficient conditions satisfying the convergence and exponential convergence of solutions for the linear system of advanced differential equations. The considered system with…
Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among the most effective first-order algorithms…
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…
The aim of this paper is to solve linear semidefinite programs arising from higher-order Lasserre relaxations of unconstrained binary quadratic optimization problems. For this we use an interior point method with a preconditioned conjugate…
In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
Composite optimization offers a powerful modeling tool for a variety of applications and is often numerically solved by means of proximal gradient methods. In this paper, we consider fully nonconvex composite problems under only local…
The (global) Lipschitz smoothness condition is crucial in establishing the convergence theory for most optimization methods. Unfortunately, most machine learning and signal processing problems are not Lipschitz smooth. This motivates us to…
Fixed point iterations are a fundamental tool in numerical analysis and scientific computing for the approximation of solutions to nonlinear problems. Their convergence is often established via the Banach fixed point theorem, provided that…
In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…
In this paper, Lipschitz univariate constrained global optimization problems where both the objective function and constraints can be multiextremal are considered. The constrained problem is reduced to a discontinuous unconstrained problem…
We present an adaptive step-size method, which does not include line-search techniques, for solving a wide class of nonconvex multiobjective programming problems on an unbounded constraint set. We also prove convergence of a general…
We fix a fundamental issue in the stochastic extragradient method by providing a new sampling strategy that is motivated by approximating implicit updates. Since the existing stochastic extragradient algorithm, called Mirror-Prox, of…
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 a variational inequality problem with a monotone and Lipschitz continuous operator in…
In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…
Stability results for extremum seeking control in $\mathbb{R}^n$ have predominantly been restricted to local or, at best, semi-global practical stability. Extending semi-global stability results of extremum-seeking systems to unbounded sets…
Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the…
It is well known that the projection method is not convergent for monotone equilibrium problems. Recently Sosa \textit{et al.} in \cite{SS2011} proposed a projection algorithm ensuring convergence for paramonotone equilibrium problems. In…
With the advancement of modern applications, an increasing number of composite optimization problems arise whose smooth component does not possess a globally Lipschitz continuous gradient. This setting prevents the direct use of the…
In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under the suitable conditions.…