Related papers: A unified differential equation solver approach fo…
This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…
The problem of constrained Markov decision process (CMDP) is investigated, where an agent aims to maximize the expected accumulated discounted reward subject to multiple constraints on its utilities/costs. A new primal-dual approach is…
This paper deals with a new Tikhonov regularized primal-dual dynamical system with variable mass and Hessian-driven damping for solving a convex optimization problem with linear equality constraints. The system features several…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…
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…
This paper is devoted to the study of an inertial accelerated primal-dual algorithm, which is based on a second-order differential system with time scaling, for solving a non-smooth convex optimization problem with linear equality…
Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…
In this paper, we study a bilinear saddle point problem of the form $\min_{x}\max_{y} F(x) + \langle Ax, y \rangle - G(y)$, where $F$ and $G$ are $\mu_F$- and $\mu_G$-strongly convex functions, respectively. By incorporating Nesterov…
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 design accelerated algorithms with improved rates for several fundamental classes of optimization problems. Our algorithms all build upon techniques related to the analysis of primal-dual extragradient methods via relative Lipschitzness…
We develop a theory of accelerated first-order optimization from the viewpoint of differential equations and Lyapunov functions. Building upon the previous work of many researchers, we consider differential equations which model the…
In Hilbert space, we propose a family of primal-dual dynamical system for affine constrained convex optimization problem. Several damping coefficients, time scaling coefficients, and perturbation terms are thus considered. By constructing…
Continuous-time primal-dual gradient dynamics (PDGD) is an ubiquitous approach for dynamically solving constrained distributed optimization problems. Yet, the distributed nature of the dynamics makes it prone to communication uncertainties,…
We analyze several generic proximal splitting algorithms well suited for large-scale convex nonsmooth optimization. We derive sublinear and linear convergence results with new rates on the function value suboptimality or distance to the…
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.…
We consider a class of multi-agent cooperative consensus optimization problems with local nonlinear convex constraints where only those agents connected by an edge can directly communicate, hence, the optimal consensus decision lies in the…
This paper studies distributed convex optimization with both affine equality and nonlinear inequality couplings through the duality analysis. We first formulate the dual of the coupling-constraint problem and reformulate it as a consensus…