Global Optimization: Interval Analysis and Balanced Interval Arithmetic

Žilinskas, Julius; Bogle, David

doi:10.1007/978-0-387-74759-0_237

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…2006). Bounds may be estimated using the interval arithmetic (Žilinskas 2005, 2006) or its modifications (Žilinskas and Bogle 2003(Žilinskas and Bogle , 2004(Žilinskas and Bogle , 2007(Žilinskas and Bogle , 2009) as well as the Lipschitz condition. The optimization stops when global optimizers are bracketed in small sub-regions guaranteeing the required accuracy.…”

Section: Branch-and-bound With a Combination Of Various Bounds For LImentioning

confidence: 99%

Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

Paulavičius¹,

Žilinskas²

2009

Technological and Economic Development of Economy

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Abstract. Many problems in economy may be formulated as global optimization problems. Most numerically promising methods for solution of multivariate unconstrained Lipschitz optimization problems of dimension greater than 2 use rectangular or simplicial branch-and-bound techniques with computationally cheap, but rather crude lower bounds. The proposed branch-and-bound algorithm with simplicial partitions for global optimization uses a combination of 2 types of Lipschitz bounds. One is an improved Lipschitz bound with the first norm. The other is a combination of simple bounds with different norms. The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well-known algorithms. The proposed algorithm often outperforms the comparable branch-and-bound algorithms.

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Section: Branch-and-bound With a Combination Of Various Bounds For LImentioning

confidence: 99%

Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

Paulavičius¹,

Žilinskas²

2009

Technological and Economic Development of Economy

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“…Several researches [1,2,9,11,15,16,32,34,35] used interval arithmetic for optimization by different techniques; interval arithmetic provides an efficient method of global optimization [10]. Interval arithmetic operations [3,[6][7][8]12,29,30] studied by several researches in various approaches and form for investigation their problem with interval in real or complex domain.…”

Section: Introductionmentioning

confidence: 99%

Parametric Functional Representation of Interval Number with Arithmetic Operations

Pal¹,

Mahapatra

2015

Int. J. Appl. Comput. Math

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The objective of this paper is to represent the interval number in different functional forms. We have represented the interval number by parametric product functional form, symmetric functional form, asymmetric functional form and convex combination functional form. We represent positive interval number in parametric product functional form, symmetric and asymmetric functional forms. However any interval number can be represented by a convex combination functional form. We also study the arithmetic operations of interval numbers based on the different forms of functional representation. Numerical examples are given to illustrate our proposed approach for arithmetic operations of the interval number in different functional form. Finally some open problems are mentioned at the end of the paper.

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The extrapolated interval global optimization algorithm

Nataraj

Sondur

2010

J Glob Optim

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Global Optimization: Interval Analysis and Balanced Interval Arithmetic

Cited by 3 publications

References 14 publications

Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

Global Optimization Using the Branch‐and‐bound Algorithm With a Combination of Lipschitz Bounds Over Simplices

Parametric Functional Representation of Interval Number with Arithmetic Operations

The extrapolated interval global optimization algorithm

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