Related papers: Subgradient algorithms for solving variable inequa…
We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
Parallel and cyclic projection algorithms are proposed for minimizing the sum of a finite family of convex functions over the intersection of a finite family of closed convex subsets of a Hilbert space. These algorithms are of…
A stochastic gradient method for finite-sum minimization subject to deterministic linear constraints is proposed and analyzed. The procedure presented adapts the projected gradient method on convex set to the use of both a stochastic…
The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…
We consider the convex minimization model with both linear equality and inequality constraints, and reshape the classic augmented Lagrangian method (ALM) by balancing its subproblems. As a result, one of its subproblems decouples the…
The data-compatibility approach to constrained optimization, proposed here, strives to a point that is "close enough" to the solution set and whose target function value is "close enough" to the constrained minimum value. These notions can…
The main contributions of this paper are the proposition and the convergence analysis of a class of inertial projection-type algorithm for solving variational inequality problems in real Hilbert spaces where the underline operator is…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
We present distributed subgradient methods for min-max problems with agreement constraints on a subset of the arguments of both the convex and concave parts. Applications include constrained minimization problems where each constraint is a…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…
We analyze the convergence of the Conjugate Gradient (CG) method in exact arithmetic, when the coefficient matrix $A$ is symmetric positive semidefinite and the system is consistent. To do so, we diagonalize $A$ and decompose the algorithm…
Locating proximal points is a component of numerous minimization algorithms. This work focuses on developing a method to find the proximal point of a convex function at a point, given an inexact oracle. Our method assumes that exact…
Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…
In this paper we present a variant of the proximal forward-backward splitting iteration for solving nonsmooth optimization problems in Hilbert spaces, when the objective function is the sum of two nondifferentiable convex functions. The…
Convex optimization problems arising in applications often have favorable objective functions and complicated constraints, thereby precluding first-order methods from being immediately applicable. We describe an approach that exchanges the…
In this paper, we are concerned with the sign-changing solutions of variational inequality problems. In order to give the existence results of the sign-changing solutions for variational inequality problems, we first construct a suitable…
We consider the problem of minimizing a convex objective which is the sum of a smooth part, with Lipschitz continuous gradient, and a nonsmooth part. Inspired by various applications, we focus on the case when the nonsmooth part is a…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…