An interval method for global nonlinear analysis

Kolev, Lubomir V.

doi:10.1109/81.847873

Cited by 33 publications

(43 citation statements)

References 21 publications

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“…A powerful idea in this area is based on the notion of successive contraction, division and elimination of some hyperrectangular regions where the solutions are sought (see e.g. [5,6,14,17,18,21]). A crucial point of this approach is a contraction method leading to bounds on the location of all the solutions contained inside a hyperrectangular region.…”

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confidence: 99%

A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

Tadeusiewicz

Hałgas

2011

Circuits Syst Signal Process

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The paper is devoted to the analysis of diode-transistor circuits having multiple DC solutions. The transistors are characterized by the Ebers-Moll model and the circuits are described by the Sandberg-Willson equation, without any piecewiselinear approximations. A new method for finding bounds on the location of all the solutions is offered. The method contracts a hyperrectangular region that includes the solutions in a systematic manner, considering in succession all the individual equations. It does not require much computation power and is very fast. The method is very useful as a preliminary step of the algorithms for finding all the DC solutions, making them more efficient. A numerical example is given to illustrate the proposed approach.

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confidence: 99%

A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

Tadeusiewicz

Hałgas

2011

Circuits Syst Signal Process

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“…An improvement of the numerical performance of the present method seems to be possible by introducing the so-called constraint propagation (exploited already in [9] for solving system of equalities) into the computational scheme of Procedure 6 of the method where systems of inequalities (22) are to be solved.…”

Section: Resultsmentioning

confidence: 99%

“…If f x ( ) is a separable function, then α i and B, which are in fact dependent on X, i.e. α α i i X = ( ) and B B X = ( ), can be determined by a procedure given in [6], [7]. This procedure is applicable both to CD components f x i ( ) of f and to continuous (C) components as well.…”

Section: New Linear Interval Linearization Of Nonlinear Functionsmentioning

confidence: 99%

“…The transformation of a nonlinear function f x ( ), x X ∈ , to the new linear interval form (4) can be done following the approach suggested in [6]- [9]. If f x ( ) is a separable function, then α i and B, which are in fact dependent on X, i.e.…”

Section: New Linear Interval Linearization Of Nonlinear Functionsmentioning

confidence: 99%

“…If f x ( ) is not in separable form, the linearization (4) is obtained in the following manner. Based on the approach adopted in [8], [9], f is first transformed equivalently into a system of q+1 functions by introducing q new auxiliary variables. More specifically…”

Section: New Linear Interval Linearization Of Nonlinear Functionsmentioning

confidence: 99%

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An interval method for global inequality-constraint optimization problems

Kolev

Penev

2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No

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-A simple interval method is suggested for globally solving optimization problems of the following type: minimize the objective function ϕ o (x) subject to the functional constraints ϕ o (x) ≤ 0, i=1,...r and the boundary constraints x∈ X (o) where x is a n-dimensional vector and X (o) is a given initial search region (a box). All the functions involved are assumed continuously differentiable in X (o) .Known interval methods for solving the global optimization problem considered are iterative and are based on a specific interval linearization of all the functions associated with the problem at each iteration of the method. This linearization involves one real term and n interval terms. In contrast, the present method appeals to a new interval linearization of each function which is constructed in such a way that now only one additive term is an interval while the remaining n terms are real numbers.The algorithm of the iterative method suggested includes the following basic procedures to be carried out at each iteration:(i) if the current subbox X is strictly feasible, then several tests for unconstrained minimization are applied and an upper bound on the global minimum is also found;(ii) if X is infeasible, X is discarded; (iii) if the first two cases do not occur, then a system of inequalities, including the objective function and some of the functional inequalities, is linearized and simultaneously solved in an attempt to reduce or completely discard X. The system involves at most n inequalities.The use of the new interval linearization in the computational scheme of the present method leads to improved performance as compared to other known interval methods of the same class. CSCC'99 Proc.pp.3661-3664

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Reliable computation of equilibrium cascades with affine arithmetic

Baharev

Rév

2008

AIChE Journal

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Computing the steady state of multistage counter-current processes like distillation, extraction, or absorption is the equivalent to finding solutions for large scale non-linear equation systems. The conventional solution techniques are fast and efficient if a good estimation is available but are prone to fail, and do not provide information about the reason for the failure. This is the main motive to apply reliable methods in solving them. Topical heading: Separations

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An interval method for global nonlinear analysis

Cited by 33 publications

References 21 publications

A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

A Contraction Method for Locating All the DC Solutions of Circuits Containing Bipolar Transistors

An interval method for global inequality-constraint optimization problems

Reliable computation of equilibrium cascades with affine arithmetic

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