Related papers: Alternating conditional gradient method for convex…

Alternating projection method has been used in a wide range of engineering applications since it is a gradient-free method (without requiring tuning the step size) and usually has fast speed of convergence. In this paper, we formalize two…

The constrained gradient method (CGM) has recently been proposed to solve convex optimization and monotone variational inequality (VI) problems with general functional constraints. While existing literature has established convergence…

We extend the result on the spectral projected gradient method by Birgin et al. in 2000 to a log-determinant semidefinite problem (SDP) with linear constraints and propose a spectral projected gradient method for the dual problem. Our…

An important method to optimize a function on standard simplex is the active set algorithm, which requires the gradient of the function to be projected onto a hyperplane, with sign constraints on the variables that lie in the boundary of…

A constrained optimization problem is primal infeasible if its constraints cannot be satisfied, and dual infeasible if the constraints of its dual problem cannot be satisfied. We propose a novel iterative method, named proportional-integral…

In this paper we consider large-scale composite optimization problems having the objective function formed as a sum of two terms (possibly nonconvex), one has (block) coordinate-wise Lipschitz continuous gradient and the other is…

This paper proposes a partially inexact alternating direction method of multipliers for computing approximate solution of a linearly constrained convex optimization problem. This method allows its first subproblem to be solved inexactly…

This paper considers the decision-dependent optimization problem, where the data distributions react in response to decisions affecting both the objective function and linear constraints. We propose a new method termed repeated projected…

In this paper, we propose a new method that combines the inexact Newton method with a procedure to obtain a feasible inexact projection for solving constrained smooth and nonsmooth equations. The local convergence theorems are established…

We present two approximate versions of the proximal subgradient method for minimizing the sum of two convex functions (not necessarily differentiable). The algorithms involve, at each iteration, inexact evaluations of the proximal operator…

In this paper, we propose a conditional gradient method for solving constrained vector optimization problems with respect to a partial order induced by a closed, convex and pointed cone with nonempty interior. When the partial order under…

This paper presents two inexact composite gradient methods, one inner accelerated and another doubly accelerated, for solving a class of nonconvex spectral composite optimization problems. More specifically, the objective function for these…

We propose an alternating subgradient method with non-constant step sizes for solving convex-concave saddle-point problems associated with general convex-concave functions. We assume that the sequence of our step sizes is not summable but…

In this paper, we investigate accelerated first-order methods for smooth convex optimization problems under inexact information on the gradient of the objective. The noise in the gradient is considered to be additive with two possibilities:…

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…

In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…

The projected subgradient method for constrained minimization repeatedly interlaces subgradient steps for the objective function with projections onto the feasible region, which is the intersection of closed and convex constraints sets, to…

In this paper, we study a class of bilevel optimization problems, also known as simple bilevel optimization, where we minimize a smooth objective function over the optimal solution set of another convex constrained optimization problem.…

In this paper, we study alternating projections on nontangential manifolds based on the tangent spaces. The main motivation is that the projection of a point onto a manifold can be computational expensive. We propose to use the tangent…

We study projection-free methods for functional constrained optimization with convex or smooth nonconvex objectives. Such problems arise in applications such as portfolio optimization and radiation therapy planning, where risk-aware…