Related papers: A DC-Reformulation for Gradient-$L^0$-Constrained …
In this paper we study the convex problem of optimizing the sum of a smooth function and a compactly supported non-smooth term with a specific separable form. We analyze the block version of the generalized conditional gradient method when…
Optimization problems with rank constraints arise in many applications, including matrix regression, structured PCA, matrix completion and matrix decomposition problems. An attractive heuristic for solving such problems is to factorize the…
We address the problem of solving convex optimization problems with many convex constraints in a distributed setting. Our approach is based on an extension of the alternating direction method of multipliers (ADMM) that recently gained a lot…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
The problem of convex optimization is studied. Usually in convex optimization the minimization is over a d-dimensional domain. Very often the convergence rate of an optimization algorithm depends on the dimension d. The algorithms studied…
Two common approaches in low-rank optimization problems are either working directly with a rank constraint on the matrix variable, or optimizing over a low-rank factorization so that the rank constraint is implicitly ensured. In this paper,…
Preconditioning has long been a staple technique in optimization, often applied to reduce the condition number of a matrix and speed up the convergence of algorithms. Although there are many popular preconditioning techniques in practice,…
This article explores distributed convex optimization with globally-coupled constraints, where the objective function is a general nonsmooth convex function, the constraints include nonlinear inequalities and affine equalities, and the…
We study a class of non-convex and non-smooth problems with \textit{rank} regularization to promote sparsity in optimal solution. We propose to apply the proximal gradient descent method to solve the problem and accelerate the process with…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Lipschitz one-dimensional constrained global optimization (GO) problems where both the objective function and constraints can be multiextremal and non-differentiable are considered in this paper. Problems, where the constraints are verified…
Distributionally robust optimization (DRO) is a widely used framework for optimizing objective functionals in the presence of both randomness and model-form uncertainty. A key step in the practical solution of many DRO problems is a…
We propose a framework to use Nesterov's accelerated method for constrained convex optimization problems. Our approach consists of first reformulating the original problem as an unconstrained optimization problem using a continuously…
The paper is devoted to a special Mirror Descent algorithm for problems of convex minimization with functional constraints. The objective function may not satisfy the Lipschitz condition, but it must necessarily have the Lipshitz-continuous…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control…
The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…
We introduce a reformulation technique that converts a many-set feasibility problem into an equivalent two-set problem. This technique involves reformulating the original feasibility problem by replacing a pair of its constraint sets with…
Most inverse optimization models impute unspecified parameters of an objective function to make an observed solution optimal for a given optimization problem with a fixed feasible set. We propose two approaches to impute unspecified…
This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is…