相关论文: An Efficient Primal-Dual Algorithm for Fair Combin…
Many algorithms in verification and automated reasoning leverage some form of duality between proofs and refutations or counterexamples. In most cases, duality is only used as an intuition that helps in understanding the algorithms and is…
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…
We present a primal-dual majorization-minimization method for solving large-scale linear programs. A smooth barrier augmented Lagrangian (SBAL) function with strict convexity for the dual linear program is derived. The…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
Models involving hybrid systems are versatile in their application but difficult to optimize efficiently due to their combinatorial nature. This work presents a method to cope with hybrid optimal control problems which, in contrast to…
In this paper, we consider solving a class of convex optimization problem which minimizes the sum of three convex functions $f(x)+g(x)+h(Bx)$, where $f(x)$ is differentiable with a Lipschitz continuous gradient, $g(x)$ and $h(x)$ have a…
Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this…
Using convex combination and linesearch techniques, we introduce a novel primal-dual algorithm for solving structured convex-concave saddle point problems with a generic smooth nonbilinear coupling term. Our adaptive linesearch strategy…
A new algorithm for solving large-scale convex optimization problems with a separable objective function is proposed. The basic idea is to combine three techniques: Lagrangian dual decomposition, excessive gap and smoothing. The main…
Based on the joint bidiagonalization process of a large matrix pair $\{A,L\}$, we propose and develop an iterative regularization algorithm for the large scale linear discrete ill-posed problems in general-form regularization: $\min\|Lx\| \…
Electricity market operators worldwide use mixed-integer linear programming to solve the allocation problem in wholesale electricity markets. Prices are typically determined based on the duals of relaxed versions of this optimization…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
In this paper, we aim at unifying, simplifying and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce the notion of nice primal algorithmic map, which plays a central…
We consider a class of multi-agent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the…
We relate the minimax game of generative adversarial networks (GANs) to finding the saddle points of the Lagrangian function for a convex optimization problem, where the discriminator outputs and the distribution of generator outputs play…
We present PDLP, a practical first-order method for linear programming (LP) designed to solve large-scale LP problems. PDLP is based on the primal-dual hybrid gradient (PDHG) method applied to the minimax formulation of LP. PDLP…
In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…
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…
We address long-standing open questions raised by Williamson, Goemans, Vazirani and Mihail pertaining to the design of approximation algorithms for problems in network design via the primal-dual method (Combinatorica 15(3):435-454, 1995).…