The Coulomb Glass - Modeling and Computational Experience with a Large Scale 0–1 QP Problem

Pörn, Ray; Nissfolk, Otto; Jansson, Fredrik; Westerlund, Tapio

doi:10.1016/b978-0-444-53711-9.50132-2

Cited by 4 publications

(1 citation statement)

References 4 publications

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“…In this case the variables can model yes or no type decisions, making these kind of problems important in various applications. MINLP models have been used in many fields including chemical and mechanical engineering, physics, medicine and, for example, in design of water/gas network [2,3,28,29,39].…”

Section: Introductionmentioning

confidence: 99%

On Mixed Integer Nonsmooth Optimization

Eronen

Westerlund

Mäkelä

2020

Numerical Nonsmooth Optimization

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In this chapter we review some deterministic solution methods for convex mixed integer nonsmooth optimization problems. The methods are branch and bound, outer approximation, extended cutting plane, extended supporting hyperplane and extended level bundle method. Nonsmoothness is taken into account by using Clarke subgradients as a substitute for the classical gradient. Ideas for convergence proofs are given as well as references where the details can be found. We also consider how some algorithms can be modified in order to solve nonconvex problems including f • -pseudoconvex functions or even f • -quasiconvex constraints.

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Section: Introductionmentioning

confidence: 99%

On Mixed Integer Nonsmooth Optimization

Eronen

Westerlund

Mäkelä

2020

Numerical Nonsmooth Optimization

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On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

Lima

Grossmann

2016

Comput Optim Appl

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Solving 0–1 Quadratic Programs by Reformulation Techniques

Pörn

Nissfolk

Skjäl

et al. 2017

Ind. Eng. Chem. Res.

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We derive and study a reformulation technique for general 0–1 quadratic programs (QP) that uses diagonal as well as nondiagonal perturbation of the objective function. The technique is an extension of the Quadratic Convex Reformulation (QCR) method developed by Billionnet and co-workers, adding nondiagonal perturbations, whereas QCR is in a sense diagonal. In this work a set of redundant reformulation-linearization technique (RLT) inequalities are included in the problem. The redundant inequalities are used to induce nondiagonal perturbations of the objective function that improve the bounding characteristics of the continuous relaxation. The optimal convexification is obtained from the solution of a semidefinite program. We apply the nondiagonal QCR (NDQCR) technique to four different types of problems and compare the bounding properties and solution times with the original QCR method. The proposed method outperforms the original QCR method on all four types of test problems.

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The Coulomb Glass - Modeling and Computational Experience with a Large Scale 0–1 QP Problem

Cited by 4 publications

References 4 publications

On Mixed Integer Nonsmooth Optimization

On Mixed Integer Nonsmooth Optimization

On the solution of nonconvex cardinality Boolean quadratic programming problems: a computational study

Solving 0–1 Quadratic Programs by Reformulation Techniques

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