Related papers: A primal-dual flow for affine constrained convex o…
The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…
This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal…
In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like primal-dual saddle-point system for the VI model in question,…
We consider the saddle point problem where the objective functions are abstract convex with respect to the class of quadratic functions. We propose primal-dual algorithms using the corresponding abstract proximal operator and investigate…
A variety of shooting methods for computing fully discrete time-periodic solutions of partial differential equations, including Newton-Krylov and optimization-based methods, are discussed and used to determine the periodic, compressible,…
This paper develops a unified distributed method for solving two classes of constrained networked optimization problems, i.e., optimal consensus problem and resource allocation problem with non-identical set constraints. We first transform…
Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primal-dual first-order method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then…
We propose decentralized primal-dual methods for cooperative multi-agent consensus optimization problems over both static and time-varying communication networks, where only local communications are allowed. The objective is to minimize the…
Second-order dynamical systems are important tools for solving optimization problems, and most of existing works in this field have focused on unconstrained optimization problems. In this paper, we propose an inertial primal-dual dynamical…
We develop two new variants of alternating direction methods of multipliers (ADMM) and two parallel primal-dual decomposition algorithms to solve a wide range class of constrained convex optimization problems. Our approach relies on a novel…
We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…
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…
We consider a primal-dual algorithm for minimizing $f(x)+h\square l(Ax)$ with Fr\'echet differentiable $f$ and $l^*$. This primal-dual algorithm has two names in literature: Primal-Dual Fixed-Point algorithm based on the Proximity Operator…
This article investigates a distributed aggregative optimization problem subject to coupled affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all…
We consider the convex-concave saddle point problem $\min_{x}\max_{y} f(x)+y^\top A x-g(y)$ where $f$ is smooth and convex and $g$ is smooth and strongly convex. We prove that if the coupling matrix $A$ has full column rank, the vanilla…
We study convex-concave saddle point problems with bilinear coupling, covering linearly constrained convex optimization and more general nonsmooth or constrained models via a proximable term in the dual objective. In linearly convergent…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We introduce a new sequential subspace optimization method for large-scale saddle-point problems. It solves iteratively a sequence of auxiliary saddle-point problems in low-dimensional subspaces, spanned by directions derived from…
This paper proposes novel primal-dual dynamical systems for solving linear equality constrained convex optimization. First, we introduce a primal-dual dynamical system with implicit Hessian damping, which can neutralize the transversal…
We consider nonsmooth optimization problems under affine constraints, where the objective consists of the average of the component functions of a large number $N$ of agents, and we only assume access to the Fenchel conjugate of the…