Quadratic Programming and Scalable Algorithms for Variational Inequalities

Dostál, Zdeněk; Horák, David; Stefanica, Dan

doi:10.1007/978-3-540-34288-5_4

Cited by 31 publications

(69 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Another conclusion of Lemma 1 is that we cannot find unique 'optimal' weights for the case of averaging over all 2 q subsets without considering more assumptions (Dostal (2009)). This may open a discussion about averaging over a set of not more than q+1 submodels only for which there are linearly independent Q 0 S matrices and for which we can find unique optimal weights versus the current common practice of averaging over all subsets resulting in a set of non-unique weights.…”

Section: Estimating the Mse And Uniqueness Of The Weightsmentioning

confidence: 98%

Minimum Mean Squared Error Model Averaging in Likelihood Models

2016

View full text Add to dashboard Cite

A data-driven method for frequentist model averaging weight choice is developed for general likelihood models. We propose to estimate the weights which minimize an estimator of the mean squared error of a weighted estimator in a local misspecification framework. We find that in general there is not a unique set of such weights, meaning that predictions from multiple model averaging estimators might not be identical. This holds in both the univariate and multivariate case. However, we show that a unique set of empirical weights is obtained if the candidate models are appropriately restricted. In particular a suitable class of models are the so-called singleton models where each model only includes one parameter from the candidate set. This restriction results in a drastic reduction in the computational cost of model averaging weight selection relative to methods which include weights for all possible parameter subsets. We investigate the performance of our methods in both linear models and generalized linear models, and illustrate the methods in two empirical applications.

show abstract

Section: Estimating the Mse And Uniqueness Of The Weightsmentioning

confidence: 98%

Minimum Mean Squared Error Model Averaging in Likelihood Models

2016

View full text Add to dashboard Cite

show abstract

“…MPRGP (Modified Proportioning and Reduced Gradient Projection) [15,8] is an efficient algorithm for solution of convex QP with simple bounds min 1 2…”

Section: Mprgpmentioning

confidence: 99%

“…a proportioning step -removes indices from the active set, 2. a conjugate gradient (CG) step -generates the next approximation in the active set if the current approximation is proportional (i.e. meeting a special criterion related to chopped, free and reduced free gradients, see [8]), 3. an expansion step -defined by the free gradient projection with a fixed steplengthᾱ, expands the active set.…”

Section: Mprgpmentioning

confidence: 99%

“…The algorithm stops, when ||g P || is sufficiently small. MPRGP has a known rate of convergence given in terms of the spectral condition number of the Hessian, and may be comparable to the cost of solution of the corresponding unconstrained QP [8].…”

Section: Mprgpmentioning

confidence: 99%

“…SMALBE (Semi-Monotonic Augmented Lagrangian with Bound and Equality) [8] is a variant of the inexact augmented Lagrangian algorithm, and can be viewed as an extension of the augmented Lagrangian method. It can be used to solve a box and equality constrained QP min 1 2…”

Section: Smalbementioning

confidence: 99%

See 2 more Smart Citations

Solving Contact Mechanics Problems with PERMON

Hapla

Horák

Pospíšil

et al. 2016

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. PERMON makes use of theoretical results in quadratic programming algorithms and domain decomposition methods. It is built on top of the PETSc framework for numerical computations. This paper describes its fundamental packages and shows their applications. We focus here on contact problems of mechanics decomposed by means of a FETI-type nonoverlapping domain decomposition method. These problems lead to inequality constrained quadratic programming problems that can be solved by our PermonQP package.

show abstract

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Dostál

Kozubek

Vlach

et al. 2015

Numerical Linear Algebra App

View full text Add to dashboard Cite

SUMMARYA cheap symmetric stiffness-based preconditioning of the Hessian of the dual problem arising from the application of the finite element tearing and interconnecting domain decomposition to the solution of variational inequalities with varying coefficients is proposed. The preconditioning preserves the structure of the inequality constraints and affects both the linear and nonlinear steps, so that it can improve the rate of convergence of the algorithms that exploit the conjugate gradient steps or the gradient projection steps. The bounds on the regular condition number of the Hessian of the preconditioned problem, which are independent of the coefficients, are given. The related stiffness scaling is also considered and analysed. The improvement is demonstrated by numerical experiments including the solution of a contact problem with variationally consistent discretization of the non-penetration conditions. The results are relevant also for linear problems.

show abstract

Quadratic Programming and Scalable Algorithms for Variational Inequalities

Cited by 31 publications

References 31 publications

Minimum Mean Squared Error Model Averaging in Likelihood Models

Minimum Mean Squared Error Model Averaging in Likelihood Models

Solving Contact Mechanics Problems with PERMON

Reorthogonalization‐based stiffness preconditioning in FETI algorithms with applications to variational inequalities

Contact Info

Product

Resources

About