Rigorous Global Search: Continuous Problems

Kearfott, R. Baker

doi:10.1007/978-1-4757-2495-0

Cited by 634 publications

(541 citation statements)

References 91 publications

(179 reference statements)

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“…Walter, 2001;Kearfott, 1996;Neumaier, 1990). Implementations of interval arithmetic and elementary functions are also readily available, and recent compilers from Sun Microsystems directly support interval arithmetic and an interval data type.…”

Section: Interval Analysis the Real Interval Vectormentioning

confidence: 99%

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Enszer

Stadtherr

2010

Progress in Industrial Mathematics at ECMI 2008

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Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for the verified solution of nonlinear dynamic models we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method used is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.

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Section: Interval Analysis the Real Interval Vectormentioning

confidence: 99%

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Enszer

Stadtherr

2010

Progress in Industrial Mathematics at ECMI 2008

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“…For the case in which f (x) is a single-use expression, that is, an expression in which each variable occurs only once, natural interval arithmetic will always yield the true function range. For cases in which obtaining a single-use expression is not possible, there are several other approaches that can be used to tighten interval extensions, 2,19,[21][22][23] including the use of Taylor models, as described in the next subsection.…”

Section: Interval Analysismentioning

confidence: 99%

Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements

Lin

Stadtherr

2007

Ind. Eng. Chem. Res.

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A strategy for state and parameter estimation in nonlinear, continuous-time systems is presented.The method provides guaranteed enclosures of all state and parameter values that are consistent with bounded-error output measurements. Key features of the method are the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of nonlinear dynamic systems with interval-valued parameters and initial states, and the use of a constraint propagation strategy on the Taylor models used to represent the solutions of the dynamic system. Numerical experiments demonstrate the use and computational efficiency of the method.

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“…Their reliability and increasing performance make them applicable to various domains such as robotics design [10], dynamic systems in robust control or robot localization [8], robust global optimization [7,12] and bounded-error parameter estimation [6].…”

Section: Introductionmentioning

confidence: 99%

Making Adaptive an Interval Constraint Propagation Algorithm Exploiting Monotonicity

Araya

Trombettoni

Neveu

2010

Lecture Notes in Computer Science

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Abstract. A new interval constraint propagation algorithm, called MOnotonic Hull Consistency (Mohc), has recently been proposed. Mohc exploits monotonicity of functions to better filter variable domains. Embedded in an interval-based solver, Mohc shows very high performance for solving systems of numerical constraints (equations or inequalities) over the reals. However, the main drawback is that its revise procedure depends on two user-defined parameters. This paper reports a rigourous empirical study resulting in a variant of Mohc that avoids a manual tuning of the parameters. In particular, we propose a policy to adjust in an auto-adaptive way, during the search, the parameter sensitive to the monotonicity of the revised function.

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Rigorous Global Search: Continuous Problems

Cited by 634 publications

References 91 publications

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Verified Solution of Nonlinear Dynamic Models in Epidemiology

Guaranteed State and Parameter Estimation for Nonlinear Continuous-Time Systems with Bounded-Error Measurements

Making Adaptive an Interval Constraint Propagation Algorithm Exploiting Monotonicity

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