Related papers: Backward Penalty Schemes for Monotone Inclusion Pr…

For a linear equality constrained convex optimization problem involving two objective functions with a ``nonsmooth" + ``nonsmooth" composite structure, we study two algorithms derived from a mixed-order dynamical system which incorporates…

Multicriterion optimization and Pareto optimality are fundamental tools in economics. In this paper we propose a new relaxation method for solving multiple objective quadratic programming problems. Exploiting the technique of the linear…

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…

We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…

We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…

We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…

This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…

We investigate the existence and uniqueness of (locally) absolutely continuous trajectories of a penalty term-based dynamical system associated to a constrained variational inequality expressed as a monotone inclusion problem. Relying on…

We give an iteration scheme for finding zeros of maximal monotone operators in Hilbert spaces. We assume that the operator is defined in the whole space. The iterates converge strongly to a solution if there exists any, otherwise they tend…

In this work, we develop a variant of a bundle method in order to find a zero of a maximal monotone operator. This algorithm relies on two polyhedral approximations of the epsilon-enlargement of the considered operator, via a systematic use…

Constrained optimization with multiple functional inequality constraints has significant applications in machine learning. This paper examines a crucial subset of such problems where both the objective and constraint functions are weakly…

In this paper, we propose a numerical approach for solving composite primal-dual monotone inclusions with a priori information. The underlying a priori information set is represented by the intersection of fixed point sets of a finite…

In this paper, we study the linear complementarity problems on the monotone extended second order cones. We demonstrate that the linear complementarity problem on the monotone extended second order cone can be converted into a mixed…

In this paper we study the convergence of an iterative algorithm for finding zeros with constraints for not necessarily monotone set-valued operators in a reflexive Banach space. This algorithm, which we call the proximal-projection method…

We establish the convergence of the forward-backward splitting algorithm based on Bregman distances for the sum of two monotone operators in reflexive Banach spaces. Even in Euclidean spaces, the convergence of this algorithm has so far…

In this article, we study inertial algorithms for numerically solving monotone inclusions involving the sum of a maximally monotone and a cocoercive operator. In particular, we analyze the convergence of inertial and relaxed versions of the…

This paper is concerned with solving nonconvex learning problems with folded concave penalty. Despite that their global solutions entail desirable statistical properties, they lack optimization techniques that guarantee global optimality in…

This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…

This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…