A multi-convex approach to latency inference and control in traffic equilibria from sparse data

Thai, Jérôme; Hariss, Rim; Bayen, Alexandre M.

doi:10.1109/acc.2015.7170815

Cited by 8 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We focus on parameterizing the cost functions of a traffic equilibrium model. Thai, Hariss, and Bayen (2015) use a mathematical program with equilibrium constraints to minimize the difference between the simulated solutions and optimal solutions to the traffic equilibrium problem as a way of recovering the specified cost function parameters. Thai and Bayen (2018) use a combination of methods by Bertsimas et al (2015) and Chen and Florian (1998) to create a multi-objective program that minimizes the duality gap for the variational inequality and the difference between the optimal and observed solutions.…”

Section: Inverse Optimization For Transportation Problemsmentioning

confidence: 99%

See 1 more Smart Citation

A Hybrid Inverse Optimization-Stochastic Programming Framework for Network Protection

Allen¹,

Terekhov²,

Gabriel³

2021

Preprint

View full text Add to dashboard Cite

Disaster management is a complex problem demanding sophisticated modeling approaches. We propose utilizing a hybrid method involving inverse optimization to parameterize the cost functions for a road network's traffic equilibrium problem and employing a modified version of Fan and Liu (2010)'s two-stage stochastic model to make protection decisions using the information gained from inverse optimization. We demonstrate the framework using two types of cost functions for the traffic equilibrium problem and show that accurate parameterizations of cost functions can change spending on protection decisions in most of our experiments.

show abstract

Section: Inverse Optimization For Transportation Problemsmentioning

confidence: 99%

“…Siri et al (2020) labels the β a as the "free flow travel times" or i.e. travel times without any interaction with other travelers [Bertsimas et al (2015); Chow et al (2014); Thai et al (2015); J. Zhang and Paschalidis (2017); J. Zhang et al (2018)].…”

Section: Different Types Of Cost Functionsmentioning

confidence: 99%

A Hybrid Inverse Optimization-Stochastic Programming Framework for Network Protection

Allen¹,

Terekhov²,

Gabriel³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed. Multi-convex problems appear in domains such as machine learning [LS99,UHZB14], signal and information processing [LS00, KP08,WYZ12], communication [SY04], and control [SGL94,HHB99,HJ14,THB15]. Typical problems in these fields include nonnegative matrix factorization (NMF) and bilinear matrix inequality (BMI) problems.…”

Section: Introductionmentioning

confidence: 99%

Disciplined multi-convex programming

Shen

Diamond

Udell

et al. 2017

2017 29th Chinese Control and Decision Conference (CCDC)

View full text Add to dashboard Cite

A multi-convex optimization problem is one in which the variables can be partitioned into sets over which the problem is convex when the other variables are fixed.Multi-convex problems are generally solved approximately using variations on alternating or cyclic minimization. Multi-convex problems arise in many applications, such as nonnegative matrix factorization, generalized low rank models, and structured control synthesis, to name just a few. In most applications to date the multi-convexity is simple to verify by hand. In this paper we study the automatic detection and verification of multi-convexity using the ideas of disciplined convex programming. We describe an implementation of our proposed method that detects and verifies multi-convexity, and then invokes one of the general solution methods. arXiv:1609.03285v2 [math.OC]

show abstract