Related papers: Primal-dual method for searching equillibriums in …
In this paper, we consider the decentralized dynamic optimization problem defined over a multi-agent network. Each agent possesses a time-varying local objective function, and all agents aim to collaboratively track the drifting global…
In this work, we design primal and dual bounding methods for multistage adaptive robust optimization (MSARO) problems motivated by two decision rules rooted in the stochastic programming literature. From the primal perspective, this is…
We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum…
In this paper, we propose a primal-dual algorithm with a novel momentum term using the partial gradients of the coupling function that can be viewed as a generalization of the method proposed by Chambolle and Pock in 2016 to solve saddle…
This paper addresses an open problem in traffic modeling: the second-order macroscopic node problem. A second-order macroscopic traffic model, in contrast to a first-order model, allows for variation of driving behavior across…
Discrete diffusion models generate structured sequences by progressively unmasking tokens, but enforcing global property constraints during generation remains an open challenge. We propose primal-dual guided decoding, an inference-time…
Variational inequality problems are recognized for their broad applications across various fields including machine learning and operations research. First-order methods have emerged as the standard approach for solving these problems due…
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…
We investigate the convergence of the primal-dual algorithm for composite optimization problems when the objective functions are weakly convex. We introduce a modified duality gap function, which is a lower bound of the standard duality gap…
Best subset selection is considered the `gold standard' for many sparse learning problems. A variety of optimization techniques have been proposed to attack this non-smooth non-convex problem. In this paper, we investigate the dual forms of…
We consider the problem of finding a low rank symmetric matrix satisfying a system of linear equations, as appears in phase retrieval. In particular, we solve the gauge dual formulation, but use a fast approximation of the spectral…
The paper proposes a variational-inequality based primal-dual dynamic that has a globally exponentially stable saddle-point solution when applied to solve linear inequality constrained optimization problems. A Riemannian geometric framework…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
When writing a constraint program, we have to choose which variables should be the decision variables, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables.…
Constrained competitive optimization involves multiple agents trying to minimize conflicting objectives, subject to constraints. This is a highly expressive modeling language that subsumes most of modern machine learning. In this work we…
A new stochastic primal--dual algorithm for solving a composite optimization problem is proposed. It is assumed that all the functions/operators that enter the optimization problem are given as statistical expectations. These expectations…
In this paper, we introduce a unified framework for studying various cloud traffic management problems, ranging from geographical load balancing to backbone traffic engineering. We first abstract these real-world problems as a…
Consider a transportation problem with sets of sources and sinks. There are profits and prices on the edges. The goal is to maximize the profit while meeting the following constraints; the total flow going out of a source must not exceed…
The alternating direction method of multipliers (ADM or ADMM) breaks a complex optimization problem into much simpler subproblems. The ADM algorithms are typically short and easy to implement yet exhibit (nearly) state-of-the-art…
Authors describe a two-stage traffic assignment model. It contains of two blocks. The first block consists of model for calculating correspondence (demand) matrix, whereas the second block is a traffic assignment model. The first model…