相关论文: Proximal gradient flow and Douglas-Rachford splitt…
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 investigate a family of approximate multi-step proximal point methods, framed as implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
In this paper, two distributed multi-proximal primal-dual algorithms are proposed to deal with a class of distributed nonsmooth resource allocation problems. In these problems, the global cost function is the summation of local convex and…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Optimal transport has recently been brought forward as a tool for modeling and efficiently solving a variety of flow problems, such as origin-destination problems and multi-commodity flow problems. Although the framework has shown to be…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper deals with composite optimization problems having the objective function formed as the sum of two terms, one has Lipschitz continuous gradient along random subspaces and may be nonconvex and the second term is simple and…
In this paper, we propose objective-function-free (OFF) variants of the proximal Newton method for nonconvex composite optimization problems and the regularized Newton method for unconstrained optimization problems, respectively, using…
In recent years, a distributed Douglas-Rachford splitting method (DDRSM) has been proposed to tackle multi-block separable convex optimization problems. This algorithm offers relatively easier subproblems and greater efficiency for…
This paper reviews the gradient sampling methodology for solving nonsmooth, nonconvex optimization problems. An intuitively straightforward gradient sampling algorithm is stated and its convergence properties are summarized. Throughout this…
This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
Proximal gradient methods are popular in sparse optimization as they are straightforward to implement. Nevertheless, they achieve biased solutions, requiring many iterations to converge. This work addresses these issues through a suitable…
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…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
This paper studies the continuous-time dynamics generated by control-theoretic Lagrangian methods for equality-constrained optimization. In particular, we consider dynamics induced by proportional-integral and feedback linearization…
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivative-free methods are proposed and developed for minimizing…
Despite its popularity in the reinforcement learning community, a provably convergent policy gradient method for continuous space-time control problems with nonlinear state dynamics has been elusive. This paper proposes proximal gradient…
We consider the problem of minimizing the sum of a smooth function $h$ with a bounded Hessian, and a nonsmooth function. We assume that the latter function is a composition of a proper closed function $P$ and a surjective linear map $\cal…