Related papers: PDHCG: A Scalable First-Order Method for Large-Sca…
Primal-dual hybrid gradient (PDHG) is a first-order method for saddle-point problems and convex programming introduced by Chambolle and Pock. Recently, Applegate et al.\ analyzed the behavior of PDHG when applied to an infeasible or…
We introduce primal and dual stochastic gradient oracle methods for decentralized convex optimization problems. Both for primal and dual oracles, the proposed methods are optimal in terms of the number of communication steps. However, for…
First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high accuracy solutions, which creates a barrier to their use in…
We propose a method to design a decentralized energy market which guarantees individual rationality (IR) in expectation, in the presence of system-level grid constraints. We formulate the market as a welfare maximization problem subject to…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
In this work, we consider a connected network of finitely many agents working cooperatively to solve a min-max problem with convex-concave structure. We propose a decentralised first-order algorithm which can be viewed as a non-trivial…
The efficient solution of large-scale multiterm linear matrix equations is a challenging task in numerical linear algebra, and it is a largely open problem. We propose a new iterative scheme for symmetric and positive definite operators,…
Recently, Deep Neural Networks (DNNs) have recorded great success in handling medical and other complex classification tasks. However, as the sizes of a DNN model and the available dataset increase, the training process becomes more complex…
We present a versatile GPU-based parallel version of Logistic Regression (LR), aiming to address the increasing demand for faster algorithms in binary classification due to large data sets. Our implementation is a direct translation of the…
This paper presents efforts to improve the hierarchical parallelism of a two scale simulation code. Two methods to improve the GPU parallel performance were developed and compared. The first used the NVIDIA Multi-Process Service and the…
This paper presents a new primal-dual method for computing an equilibrium of generalized (continuous) Nash game (referred to as generalized Nash equilibrium problem (GNEP)) where each player's feasible strategy set depends on the other…
In this paper a robust second-order method is developed for the solution of strongly convex l1-regularized problems. The main aim is to make the proposed method as inexpensive as possible, while even difficult problems can be efficiently…
A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different…
In this paper we propose a distributed dual gradient algorithm for minimizing linearly constrained separable convex problems and analyze its rate of convergence. In particular, we prove that under the assumption of strong convexity and…
Planning long-horizon robot manipulation requires making discrete decisions about which objects to interact with and continuous decisions about how to interact with them. A robot planner must select grasps, placements, and motions that are…
We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.…
In the area of matching-based market design, existing models using cardinal utilities suffer from two deficiencies: First, the Hylland-Zeckhauser (HZ) mechanism, which has remained a classic in economics for one-sided matching markets, is…
This work focuses on a class of general decentralized constraint-coupled optimization problems. We propose a novel nested primal-dual gradient algorithm (NPGA), which can achieve linear convergence under the weakest known condition, and its…
In this paper, we consider solving a composite optimization problem with coupling constraints in a multi-agent network based on proximal gradient method. In this problem, all the agents jointly minimize the sum of individual cost functions…
Linear programming (LP) relaxation is a standard technique for solving hard combinatorial optimization (CO) problems. Here we present a gradient descent algorithm which exploits the special structure of some LP relaxations induced by CO…