Related papers: A Technical Note on the Implementation and Use of …

We introduce cuPDLPx, a further enhanced GPU-based first-order solver for linear programming. Building on the recently developed restarted Halpern PDHG for LP, cuPDLPx incorporates a number of new techniques, including a new restart…

First-order methods for solving convex optimization problems have been at the forefront of mathematical optimization in the last 20 years. The rapid development of this important class of algorithms is motivated by the success stories…

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…

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

This paper is devoted to the design of efficient primal-dual algorithm (PDA) for solving convex optimization problems with known saddle-point structure. We present a new PDA with larger acceptable range of parameters and correction, which…

In this paper we present the solver DuQuad specialized for solving general convex quadratic problems arising in many engineering applications. When it is difficult to project on the primal feasible set, we use the (augmented) Lagrangian…

In this paper we are interested in the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. CS problems of this type are convex with non-smooth and non-separable…

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…

Quadratic cone programs are rapidly becoming the standard canonical form for convex optimization problems. In this paper we address the question of differentiating the solution map for such problems, generalizing previous work for linear…

These notes focus on the minimization of convex functionals using first-order optimization methods, which are fundamental in many areas of applied mathematics and engineering. The primary goal of this document is to introduce and analyze…

In this chapter we derive computational complexity certifications of first order inexact dual methods for solving general smooth constrained convex problems which can arise in real-time applications, such as model predictive control. When…

Domain-Driven Solver (DDS) is a MATLAB-based software package for convex optimization problems in Domain-Driven form [Karimi and Tun\c{c}el, arXiv:1804.06925]. The current version of DDS accepts every combination of the following…

Linear Programming (LP) is a foundational optimization technique with widespread applications in finance, energy trading, and supply chain logistics. However, traditional Central Processing Unit (CPU)-based LP solvers often struggle to meet…

Recent enhancements to the Primal-Dual Hybrid Gradient (PDHG) algorithm have enabled GPUs to efficiently solve large linear programming problems, often faster than the long-dominant simplex and interior-point methods. The solutions found by…

We present a distributed framework of the Primal-Dual Hybrid Gradient (PDHG) algorithm for solving massive-scale linear programming (LP) problems. Although PDHG-based solvers demonstrate strong performance on single-node GPU architectures,…

In this paper we are concerned with the solution of Compressed Sensing (CS) problems where the signals to be recovered are sparse in coherent and redundant dictionaries. We extend a primal-dual Newton Conjugate Gradients (pdNCG) method for…

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…

Robot programming tools ranging from inverse kinematics (IK) to model predictive control (MPC) are most often described as constrained optimization problems. Even though there are currently many commercially-available second-order solvers,…

Primal-dual hybrid gradient method (PDHG, a.k.a. Chambolle and Pock method) is a well-studied algorithm for minimax optimization problems with a bilinear interaction term. Recently, PDHG is used as the base algorithm for a new LP solver…

In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…