Hildreth’s algorithm with applications to soft constraints for user interface layout

Jamil, Noreen; Chen, Xuemei; Cloninger, Alexander

doi:10.1016/j.cam.2015.04.014

Cited by 18 publications

(9 citation statements)

References 33 publications

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“…Since in our case there are O(n 3 ) constraints, we find that, in practice, this averaging approach leads to changes that are so small that no meaningful progress can be made from one iteration to the next. The challenge in using a randomized approach (see [35]) is that visiting constraints at random leads to a much higher cost for visiting the same number of constraints. This is because accessing dual variables at random from a dictionary is slower in practice than sequentially visiting elements in an array of dual variables.…”

Section: Discussion and Future Challengesmentioning

confidence: 99%

A Projection Method for Metric-Constrained Optimization

Veldt,

Gleich,

Wirth

et al. 2018

Preprint

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We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine learning applications and theoretical approximation algorithms for graph clustering. Although these problem are interesting from a theoretical perspective, they are challenging to solve in practice due to the high memory requirement of black-box solvers. In order to address this challenge we first prove that the metric-constrained linear program relaxation of correlation clustering is equivalent to a special case of the metric nearness problem. We then developed a general solver for metric-constrained linear and quadratic programs by generalizing and improving a simple projection algorithm originally developed for metric nearness. We give several novel approximation guarantees for using our framework to find lower bounds for optimal solutions to several challenging graph clustering problems. We also demonstrate the power of our framework by solving optimizing problems involving up to 10 8 variables and 10 11 constraints.

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Section: Discussion and Future Challengesmentioning

confidence: 99%

A Projection Method for Metric-Constrained Optimization

Veldt,

Gleich,

Wirth

et al. 2018

Preprint

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“…As mentioned previously, much of the focus on this problem has been in the error correction and compressed sensing literature [FR13,EK12]. However, there has been work that has focused on iterative row-action methods; previous work in this direction includes [HN18a,JCC15,ABH05].…”

Section: Related Workmentioning

confidence: 99%

Quantile-based Iterative Methods for Corrupted Systems of Linear Equations

Haddock¹,

Needell²,

Rebrova³

et al. 2020

Preprint

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Often in applications ranging from medical imaging and sensor networks to error correction and data science (and beyond), one needs to solve large-scale linear systems in which a fraction of the measurements have been corrupted. We consider solving such large-scale systems of linear equations Ax = b that are inconsistent due to corruptions in the measurement vector b. We develop several variants of iterative methods that converge to the solution of the uncorrupted system of equations, even in the presence of large corruptions. These methods make use of a quantile of the absolute values of the residual vector in determining the iterate update. We present both theoretical and empirical results that demonstrate the promise of these iterative approaches. * The authors were partially supported by NSF CAREER #1348721 and NSF BIGDATA #1740325. We also acknowledge sponsorship by Capital FundManagement.

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“… Hildreth's quadratic programming : it is the method used to solve the constrained optimization problem in this article. It is because Hildreth's algorithm is an efficient method for solving large systems of inequalities with sparse matrices, 30 and also it does not require any matrix inversion. This quadratic programming is used at each sampling time, having obtained a vector

λ \geq 0

that is called dual variables in the optimization literature.…”

Section: Constrained Control In Ldmpc Design Using Laguerre Functionmentioning

confidence: 99%

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

Pinheiro

Silveira

2020

Optim Control Appl Methods

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SummaryThis work presents a multivariable predictive controller applied on a redundant robotic manipulator with three degrees of freedom. The article focuses on the design of a discrete model‐based predictive controller (DMPC) using the Laguerre function as a control effort weighting method to enhance the solution of Hildreth's quadratic programming and to minimize the trade‐off problem in constrained case. The Laguerre functions are used to simplify and enhance the control horizon effect through parsimonious control trajectory, thus reducing the computational load required to find the optimal control solution. Furthermore, these results can be confirmed by simulations and experimental tests on the manipulator and comparing it to the traditional DMPC approach and the discrete linear quadratic regulator.

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Hildreth’s algorithm with applications to soft constraints for user interface layout

Cited by 18 publications

References 33 publications

A Projection Method for Metric-Constrained Optimization

A Projection Method for Metric-Constrained Optimization

Quantile-based Iterative Methods for Corrupted Systems of Linear Equations

Constrained discrete model predictive control of an arm‐manipulator using Laguerre function

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