The ‘Idiot’ crash quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

Galabova, I. L.; Hall, Julian

doi:10.1080/10556788.2019.1604702

Cited by 7 publications

(4 citation statements)

References 10 publications

(12 reference statements)

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“…These four problems are relaxations of quadratic assignment problems [59], a classical NP-hard combinatorial optimization problem. These instances are known to be challenging for traditional solvers and amenable to first-order methods [22]. The instance sizes are given in Table 3.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness

Applegate¹,

Hinder²,

Lu³

et al. 2021

Preprint

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Primal-dual first-order methods such as ADMM (alternating direction method of multipliers), PDHG (primal-dual hybrid gradient method) and EGM (extra-gradient method) are often slow at finding high accuracy solutions, particularly when applied to linear programs. This paper analyzes sharp primal-dual problems, a strict generalization of linear programming. We show that for sharp primal-dual problems, many primal-dual first-order methods achieve linear convergence using restarts. For PDHG on bilinear games, we prove that the convergence bounds improve from Θ(κ 2 log(1/ )) to Θ(κ log(1/ )) through the use of restarts where κ is the condition number and is the desired accuracy. Moreover, the latter rate is optimal for wide class of primal-dual methods. We develop an adaptive restart scheme and verify that restarts significantly improve the ability of PDHG to find high accuracy solutions to linear programs.

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Section: Numerical Experimentsmentioning

confidence: 99%

Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness

Applegate¹,

Hinder²,

Lu³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The main idea of ICA [Galabova and Hall, 2020] is to relax the original LP problem to an approximate problem with "soft" constraint, and then solve this relaxed problem to obtain a near-optimal point. This point is later used as the starting point of the simplex method for solving the original problem.…”

Section: Idiot Crash Algorithm (Ica)mentioning

confidence: 99%

Simplex Initialization: A Survey of Techniques and Trends

Huang¹,

Zhong²,

Yang³

et al. 2021

Preprint

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The simplex method is one of the most fundamental technologies for solving linear programming (LP) problems and has been widely applied to different practical applications. In the past literature, how to improve and accelerate the simplex method has attracted plenty of research. One important way to achieve this goal is to find a better initialization method for the simplex. In this survey, we aim to provide an overview about the initialization methods in the primal and dual simplex, respectively. We also propose several potential future directions about how to improve the existing initialization methods with the help of advanced learning technologies.

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“…These two problems are relaxations of quadratic assignment problems [28], a classical NP-hard combinatorial optimization problem. These instances are known to be challenging for traditional solvers and amenable to first-order methods [29].…”

Section: Quadratic Assignment Problem Relaxationsmentioning

confidence: 99%

A generic adaptive restart scheme with applications to saddle point algorithms

Hinder¹,

Lubin²

2020

Preprint

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We provide a simple and generic adaptive restart scheme for convex optimization that is able to achieve worst-case bounds matching (up to constant multiplicative factors) optimal restart schemes that require knowledge of problem specific constants. The scheme triggers restarts whenever there is sufficient reduction of a distance-based potential function. This potential function is always computable. We apply the scheme to obtain the first adaptive restart algorithm for saddle-point algorithms including primal-dual hybrid gradient (PDHG) and extragradient. The method improves the worst-case bounds of PDHG on bilinear games, and numerical experiments on quadratic assignment problems and matrix games demonstrate dramatic improvements for obtaining high-accuracy solutions. Additionally, for accelerated gradient descent (AGD), this scheme obtains a worst-case bound within 60% of the bound achieved by the (unknown) optimal restart period when high accuracy is desired. In practice, the scheme is competitive with the heuristic of O'Donoghue and Candes [1].Preprint. Under review.

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The ‘Idiot’ crash quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

Cited by 7 publications

References 10 publications

Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness

Faster First-Order Primal-Dual Methods for Linear Programming using Restarts and Sharpness

Simplex Initialization: A Survey of Techniques and Trends

A generic adaptive restart scheme with applications to saddle point algorithms

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