Related papers: On Solving Convex Optimization Problems with Linea…

This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…

This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…

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…

The forward-backward operator splitting algorithm is one of the most important methods for solving the optimization problem of the sum of two convex functions, where one is differentiable with a Lipschitz continuous gradient and the other…

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…

Nonconvex sparse models have received significant attention in high-dimensional machine learning. In this paper, we study a new model consisting of a general convex or nonconvex objectives and a variety of continuous nonconvex…

This paper deals with constrained convex problems, where the objective function is smooth strongly convex and the feasible set is given as the intersection of a large number of closed convex (possibly non-polyhedral) sets. In order to deal…

In this paper, we consider a nonsmooth convex finite-sum problem with a conic constraint. To overcome the challenge of projecting onto the constraint set and computing the full (sub)gradient, we introduce a primal-dual incremental gradient…

This paper studies a class of simple bilevel optimization problems where we minimize a composite convex function at the upper-level subject to a composite convex lower-level problem. Existing methods either provide asymptotic guarantees for…

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates ${u_n}$ converges weakly to a point in the…

The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…

We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…

In this work, we focus on separable convex optimization problems with linear and box constraints and compute the solution in closed-form as a function of some Lagrange multipliers that can be easily computed in a finite number of…

This paper studies the distributed optimization problem when the objective functions might be nondifferentiable and subject to heterogeneous set constraints. Unlike existing subgradient methods, we focus on the case when the exact…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Convex optimization models find interesting applications, especially in signal/image processing and compressive sensing. We study some augmented convex models, which are perturbed by strongly convex functions, and propose a dual gradient…

In this paper, we introduce faster accelerated primal-dual algorithms for minimizing a convex function subject to strongly convex function constraints. Prior to our work, the best complexity bound was $\mathcal{O}(1/{\varepsilon})$,…

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…

We study alternating first-order algorithms with no inner loops for solving nonconvex-strongly-concave min-max problems. We show the convergence of the alternating gradient descent--ascent algorithm method by proposing a substantially…

We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…