Related papers: On efficiently solving the subproblems of a level-…

This work is concerned with the efficient optimization method for solving a large class of optimal mass transport problems. An inexact primal-dual algorithm is presented from the time discretization of a proper dynamical system, and by…

In this paper, we propose a Newton method for unconstrained set optimization problems to find its weakly minimal solutions with respect to lower set-less ordering. The objective function of the problem under consideration is given by…

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

Many of the algorithms used to solve minimization problems with sparsity-inducing regularizers are generic in the sense that they do not take into account the sparsity of the solution in any particular way. However, algorithms known as…

The use of the fractional Laplacian in image denoising and regularization of inverse problems has enjoyed a recent surge in popularity, since for discontinuous functions it can behave less aggressively than methods based on $H^1$ norms,…

For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods sequentially minimize a Lagrangian function subject to linearized constraints. These methods converge rapidly near a solution but may not be…

We introduce a quadratically convergent semismooth Newton method for nonlinear semidefinite programming that eliminates the need for the generalized Jacobian regularity, a common yet stringent requirement in existing approaches. Our…

We propose a new fast algorithm for solving one of the standard approaches to ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth) regularizer is minimized under the constraint that the solution explains the observations…

We contribute improvements to a Lagrangian dual solution approach applied to large-scale optimization problems whose objective functions are convex, continuously differentiable and possibly nonlinear, while the non-relaxed constraint set is…

Recently, lower-level constrained bilevel optimization has attracted increasing attention. However, existing methods mostly focus on either deterministic cases or problems with linear constraints. The main challenge in stochastic cases with…

Level-set methods for convex optimization are predicated on the idea that certain problems can be parameterized so that their solutions can be recovered as the limiting process of a root-finding procedure. This idea emerges time and again…

We present a new feasible proximal gradient method for constrained optimization where both the objective and constraint functions are given by the summation of a smooth, possibly nonconvex function and a convex simple function. The…

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a…

In this paper, we study the equality constrained nonlinear least squares problem, where the Jacobian matrices of the objective function and constraints are unavailable or expensive to compute. We approximate the Jacobian matrices via…

Feature selection is an important and active research area in statistics and machine learning. The Elastic Net is often used to perform selection when the features present non-negligible collinearity or practitioners wish to incorporate…

In this paper, we consider the nonsmooth convex optimization problems over the fixed point constraint sets of firmly nonexpansive operators. To find an optimal solution of the problem, we present an iterative method based on the hybrid…

In this paper, we present a new ellipsoid-type algorithm for solving nonsmooth problems with convex structure. Examples of such problems include nonsmooth convex minimization problems, convex-concave saddle-point problems and variational…

In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving…

We know that compressive sensing can establish stable sparse recovery results from highly undersampled data under a restricted isometry property condition. In reality, however, numerous problems are coherent, and vast majority conventional…

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient.…