R. Baker Kearfott. Rigorous Global Search: Continuous Problems. Kluwer, October 1996. Home/Search Document Not in Database Summary Related Articles Check |
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Fault Detection Based on Interval Models and.. - Armengol.. (2001) (Correct)
....problem. The function whose range has to be determined is the interval model of the system and the parameter space is determined by the interval values of the parameters of the model, the inputs and the initial state. This problem can be solved, for instance, using global optimization algorithms [4, 5]. This task needs, most of the times, an important computation effort and, even in this case, the results usually are only approximations to the exact values due to errors of rounding, truncation, etc. Therefore, the result of the simulation usually is not the envelope but an approximation of it, ....
R. Kearfott. Rigorous global search: continuous problems. Kluwer Academic Publishers, 1996.
Interval Analysis for Thermodynamic Calculations in Process.. - Hua, al. (1998) (Correct)
....; X 2 ; X n ) T has n real interval components and can be interpreted geometrically as an n dimensional rectangle. Note that in this section lower case quantities are real numbers and upper case quantities are intervals. Several good introductions to computation with intervals are available [3,4,5]. Of particular interest here are interval Newton generalized bisection (IN GB) methods. These techniques provide the power to find, with confidence, enclosures of all solutions of a system of nonlinear equations [3,5] and to find with total reliability the global minimum of a nonlinear ....
....Several good introductions to computation with intervals are available [3,4,5] Of particular interest here are interval Newton generalized bisection (IN GB) methods. These techniques provide the power to find, with confidence, enclosures of all solutions of a system of nonlinear equations [3,5], and to find with total reliability the global minimum of a nonlinear objective function [4] provided only that upper and lower bounds are available for all variables. For a system of nonlinear equations f(x) 0 with x 2 X (0) the basic iteration step in interval Newton methods is, given an ....
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R. B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996.
High Performance Computing: Are We Just Getting Wrong.. - Mark Stadtherr.. (Correct)
.... there do exist methods, based on interval mathematics, in particular interval Newton methods, that can, given initial bounds on the variables, enclose any and all solutions to a nonlinear equation system, or determine that there is no solution, or find the global optimum of a nonlinear function [5]. These methods provide a mathematical and also computational guarantee of reliability. The latter is important since mathematical guarantees can be lost once things are implemented in floating point arithmetic. In my group at Notre Dame, we are actively involved in developing algorithms and ....
R. B. Kearfott. Rigorous Global Search: Continuous Problems, Kluwer (1996).
Generalized Subinterval Selection Criteria for Interval Global.. - Csendes (Correct)
....minimum value of the function f(x) on the search region X by f . Assume that we have an isotone inclusion function F (X) for f(x) Several Branch and Bound (B B) type algorithms have been suggested and studied for the solution of (1) utilizing inclusion function information on the problem [9, 11, 15]. To allow a general discussion, we study the following algorithm framework that can incorporate most of the features of the present procedures. 2 Algorithm Step 1 Let L be an empty list, the leading box A : X, and the iteration counter k : 1. Set f = F (X) Step 2 Subdivide A into s ....
R. B. Kearfott, Rigorous global search: continuous problems, Kluwer, Dordrecht, 1996.
Probabilities, Intervals, What Next? Optimization Problems.. - Kreinovich (2003) (Correct)
.... is that y belongs to the range y = y; y] of the function f over the box x 1 Theta : Theta x n : y = y; y] ff(x 1 ; x n ) j x 1 2 x 1 ; x n 2 x n g: The process of computing this interval range based on the input intervals x i is called interval computations; see, e.g. [5, 6, 7, 12]. Interval computations as an optimization problem. The main problem of interval computations can be naturally reformulated as an optimization problem. Indeed, y is the solution to the following problem: f(x 1 ; x n ) min; under the conditions x 1 x 1 x 1 ; x n x n x n ; ....
Kearfott R. B. (1996), "Rigorous Global Search: Continuous Problems", Kluwer, Dordrecht.
Fast Quantum Algorithms for Handling.. - Martinez.. (2003) (Correct)
....to compute this mean with accuracy in 1= iterations; so, for accuracy 20 , we only need 5 iterations. Since computing f may take a long time, this drastic (5 times) speed up may be essential. 4 Quantum Algorithms for Interval Computations Problem. In interval computations (see, e.g. [9, 10, 14]) the main objective is as follows. Given: ffl intervals [x i ; x i ] of possible values of the inputs x 1 ; xn , and compute the exact range [y; y] of possible values of y. We can describe each interval in a more traditional form [ex i Gamma Delta i ; e x i Delta i ] 4) where ....
R. B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht, 1996.
An Improved Method for the Computation of Affine Lower Bound.. - Garloff (2003) (1 citation) (Correct)
....best underestimating convex functions, cf. 3, 9, 12] Because of their simplicity and ease of computation, constant and ane lower bound functions are especially useful. Constant bound functions are thoroughly used when interval computation techniques are applied to global optimization, cf. [7, 8, 11]. However, when using constant bound functions, all information about the shape of the given function is lost. A compromise between convex envelopes, which require in the general case much computational e ort, and constant lower bound functions are ane lower bound functions. In [5] we concentrate ....
Kearfott R. B. (1996), \Rigorous Global Search: Continuous Problems," Series Nonconvex Optimization and its Applications Vol. 13, Kluwer Acad. Publ., Dordrecht, Boston, London.
Determination of Properties of Composite Materials - From The Lamb (2003) (Correct)
.... from measurements, and measurements are never 100 accurate: ffl there is a random measurement error component, which corresponds to a probabilistic uncertainty; see, e.g. 11] ffl there are known bounds on a systematic error component, which correspond to interval uncertainty; see, e.g. [2, 4, 6]; ffl in addition to these bounds in which experts are absolutely sure, experts have smaller bounds with reasonable but not absolute certainty; these bounds are naturally described by fuzzy techniques; see, e.g. 1, 5, 10] 2. Case Study: Monoclinic Transverse Isotropic Material Let us first ....
....error (this way, we do not miss the correct value) and test all values C grid. The main problem with this approach is that is still takes too much time. 5. Inverse Problem Under Interval and Fuzzy Uncertainty: Formulation Case of interval uncertainty. For interval uncertainty (see, e.g. [2, 4, 6]) the only information that we have about the error with which we measure velocity c is the upper bound ffi on this measurement error. In this case, it is natural to look for the values C pq for which, for every measurement k, pq )j ffi: 31) Comment on interval uncertainty. In the ....
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R. B. Kearfott, Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht, 1996.
On the Complexity of Isolating Real Roots and Computing with.. - Mourrain, al. (2002) (2 citations) (Correct)
....they are particularly useful when the function F n , is not smooth or cannot be accurately evaluated. Also, another class of bisection methods, based on interval analysis, has been widely used. These methods are robust and appropriate for finding starting points for Newton like methods (see, e.g. [24 26, 28, 30, 37]) The accurate computation of topological degree of the mapping F n at G n relative to the bounded domain D n , using Stenger s or other related methods [22, 23, 52, 53] is heavily based on suitable assumptions, including the appropriate representation of the oriented boundary of D n . In ....
....attracted the attention of many research efforts and, as a result, many different approaches to the problem exist. We briefly mention here the deflation techniques used for the calculation of further solutions [7] or other more efficient and more recent interval analysis based methods (see, e.g. [15, 16, 26, 28, 30, 37]) and the methods described in [20, 21, 41] The corresponding existence tool of interval analysis based methods is the availability of the range of the function in a given interval, which can be implemented using interval arithmetic, though range overestimation, and hence efficiency problems must ....
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R. B. Kearfott, "Rigorous Global Search: Continuous Problems," Kluwer Academic, Dordrecht, 1996.
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....rigorous veri cation of feasibility, constraint satisfaction, global optimization, degeneracy, redundant constraints 2000 MSC Classi cation: primary 90C30, secondary 62F30, 65G20 1. Introduction In rigorous constrained global optimization algorithms (see, e.g. the books by Kearfott [4], Ratschek Rokne [7] and van Hentenryck et al. 8] it is necessary to verify that close to an approximate, putative optimal point there is a feasible point satisfying all constraints with certainty. To do this, the existence theory associated with Krawczyk s operator (derived in [5, Chapter ....
Kearfott, R. B.: Rigorous Global Search: Continuous Problems, Kluwer, Dordrecht, 1996.
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