Related papers: Dynamical Primal-Dual Accelerated Method with Appl…
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…
We consider strongly convex optimization problems with affine-type restrictions. We build dual problem and solve dual problem by Fast Gradient Method. We use primal-dual structure of this method to construct the solution of the primal…
We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in \cite{vu} for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators…
We propose primal-dual stochastic mirror descent for the convex optimization problems with functional constraints. We obtain the rate of convergence in terms of probability of large deviations.
This work studies nonconvex distributed constrained optimization over stochastic communication networks. We revisit the distributed dual averaging algorithm, which is known to converge for convex problems. We start from the centralized…
This paper considers a distributed convex optimization problem over a time-varying multi-agent network, where each agent has its own decision variables that should be set so as to minimize its individual objective subject to local…
We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in…
In this paper we propose a randomized primal-dual proximal block coordinate updating framework for a general multi-block convex optimization model with coupled objective function and linear constraints. Assuming mere convexity, we establish…
In this paper, we focus on an asynchronous distributed optimization problem. In our problem, each node is endowed with a convex local cost function, and is able to communicate with its neighbors over a directed communication network.…
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 propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates,…
This paper investigates the asymptotic and non-asymptotic behavior of the quantized primal dual algorithm in network utility maximization problems, in which a group of agents maximize the sum of their individual concave objective functions…
Dual first-order methods are powerful techniques for large-scale convex optimization. Although an extensive research effort has been devoted to studying their convergence properties, explicit convergence rates for the primal iterates have…
Distributed optimization algorithms are essential for training machine learning models on very large-scale datasets. However, they often suffer from communication bottlenecks. Confronting this issue, a communication-efficient primal-dual…
Optimal power flow (OPF) is an important problem for power generation and it is in general non-convex. With the employment of renewable energy, it will be desirable if OPF can be solved very efficiently so its solution can be used in real…
We extend a primal-dual fixed point algorithm (PDFP) proposed in [5] to solve two kinds of separable multi-block minimization problems, arising in signal processing and imaging science. This work shows the flexibility of applying PDFP…
In this paper we consider a distributed convex optimization problem over time-varying networks. We propose a dual method that converges R-linearly to the optimal point given that the agents' objective functions are strongly convex and have…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
We examine stability properties of primal-dual gradient flow dynamics for composite convex optimization problems with multiple, possibly nonsmooth, terms in the objective function under the generalized consensus constraint. The proposed…
We introduce a randomly extrapolated primal-dual coordinate descent method that adapts to sparsity of the data matrix and the favorable structures of the objective function. Our method updates only a subset of primal and dual variables with…