INTLAB implementation of an interval global optimization algorithm

Pál, László; Csendes, Tibor

doi:10.1080/10556780902753395

Cited by 12 publications

(11 citation statements)

References 13 publications

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“…Interval arithmetic techniques are also the basis of the GloptLab solver developed by Domes [8] for quadratic constraint satisfaction problems and the global solver developed by Pál and Csendes [20] for bound-constrained global optimization problems. The GloptiPoly 3 solver developed by Didier et al [7] relies on semidefinite programming techniques and solves the generalized problem of moments, an infinite-dimensional optimization problem that subsumes the problem of global optimization over polynomials.…”

Section: Part 2 -Computations and Softwarementioning

confidence: 99%

Global optimization

Sahinidis

2009

Optimization Methods and Software

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The optimization community has long been interested in solving multiextremal optimization problems to global optimality. Some of the first exact approaches to nonconvex nonlinear programs (NLPs) and mixed-integer nonlinear programs (MINLPs) relied on convexification via cutting planes [23], as well as branch-and-bound, i.e. bounding combined with progressive partitioning of the space of continuous, in addition to integer, variables [9]. Approximations based on the a priori discretization of nonlinear functions were also proposed and capitalized on the availability of fast linear integer programming techniques [3]. Activities in the field of global optimization started to intensify in the early 1990s, when the Journal of Global Optimization was launched. Today, the global optimization community has grown considerably, as evidenced by flourishing publications and conference activities in this area. The book by Horst and Tuy [11], an indispensable resource for anyone working in this area, has received over 1200 citations (according to Google Scholar as of 17 June 2009). At the same time, the 20th International Symposium on Mathematical Programming (Chicago, 2009) is scheduled to include 20 sessions in its global optimization cluster, with many additional related sessions in its MINLP cluster. Clearly, global optimization has grown into an area of major focus in the field of mathematical programming over the past two decades.The purpose of this special issue is to showcase current research activities in the area of global optimization. The papers of this issue reflect the broad range of activities in this area and address deterministic as well as stochastic algorithms, the development of software and computational experience with a variety of algorithms, and a number of applications in engineering and science. Corresponding to these three thematic areas, the papers have been grouped into three parts. Part 1 -Theory and algorithmsIn the first part, there are five papers that present and analyse, mostly theoretically, a variety of algorithms and methodologies:• Contrary to the widespread practice of building relaxations of nonconvex problems by outer approximating one term of a nonconvex constraint at a time, Bao et al. [2] investigate relaxations that consider multiple terms simultaneously.

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Section: Part 2 -Computations and Softwarementioning

confidence: 99%

Global optimization

Sahinidis

2009

Optimization Methods and Software

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“…As compared to the numerical study published in Pál and Csendes [83] and presented later in Section 3.3.3, where the stopping criterion parameter ϵ was set to 10 −8 , now we stopped the subdivision when the width of the inclusion function at the actual subinterval was less than 0.01. Our present results are then obviously much weaker than the earlier published ones, but it is no wonder regarding that in the other case rst and second derivative information was utilized as well.…”

Section: Numerical Tests and Resultsmentioning

confidence: 99%

“…We discuss here just the larger and systematic dierences. The most signicant change is denitely in the CPU time needed: the INTLAB based implementa- [83] and later in Section 3.3.3). The highest ratio values are related to cases when the CPU time for the C-XSC version were hardly measurably low.…”

Section: Numerical Tests and Resultsmentioning

confidence: 99%

“…This method originates in the Numerical Toolbox for Veried Computing (see Hammer et al [46]), and it applies only a single accelerating device: the cuto test in contrast to the more sophisticated techniques studied in Pál and Csendes [83]. Now just natural interval extension (based on naive interval arithmetic) was applied to calculate the inclusion functions.…”

Section: Description and Implementationmentioning

confidence: 99%

“…This chapter deals with interval based global optimization algorithms and it is based on three papers: Csendes and Pál [32], Pál and Csendes [83], and Pál and Csendes [85].…”

Section: Introductionmentioning

confidence: 99%

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