R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers, preprint, 1995. Home/Search Document Details and Download
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Treating Non-Smooth Functions as Smooth Functions in Global.. - Kearfott (1995) (1 citation) Self-citation (Kearfott) (Correct)
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R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers, preprint, 1995.
Interval Robustness in Nonsmooth Nonlinear Parameter.. - Muñoz, Kearfott (2001) Self-citation (Kearfott) (Correct)
.... is available from Kearfott [6] Hansen [2] Neumaier [8] Special algorithms developed in GlobSol handle non smooth problems such as l 1 and l 1 optimizations with 3 the same techniques as smooth problems, and under certain conditions the interval Newton method converges linearly (See Kearfott [4], 5] Ratz [10] In practice, the interval Newton procedure can also be combined with an interval branch and bound technique, so that roots of g( 0 that cannot be the global minimum need not be found. The solution algorithm is applied to a sequence of intervals, beginning with some initial ....
R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers. Computing, 57:149-162, 1996.
Slope Interval, Generalized Gradient, Semigradient, and.. - Kearfott, Muñoz (2001) (2 citations) Self-citation (Kearfott) (Correct)
.... to obtain S ] f; x; x) Interval Newton iteration with slope intervals can be e ective in global optimization and nonlinear systems solvers, especially when the derivatives of the objective function f have jump discontinuities, such as when f contains terms involving k k or max, [6], 7] 16] 20] Lemma 2.2. Let f : R R, and let x be an interval vector containing x. Then the limiting slope interval is given by lim w(x) 0 S ] f; x; x) lim inf x x f(x) f( x) x x ; lim sup x x f(x) f( x) x x = m; M ] Proof. By de nition, S ] f; x; x) is ....
R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers. Computing, 57:149-162, 1996.
Treating Non-Smooth Functions as Smooth Functions in Global.. - Kearfott (1995) (1 citation) Self-citation (Kearfott) (Correct)
....without conditional branches. In fact, however, many practical problems, in particular those containing expressions such as jE(X)j and maxfE(X) F (X)g, E; F : R n R, or expressions defined by IF THEN ELSE branches, result in functions whose derivatives have jump discontinuities. However, in [4], continuous, order 1 interval extensions were proposed for such continuous but non smooth functions. Such interval extensions of non smooth functions can be used in the same contexts as other interval extensions. However, the width of a non smooth derivative extension F 0 (X) or slope ....
....advantage of treating such non smooth problems with the same techniques as smooth problems. This simpler, unified treatment is possible within the context described in this paper. First, required properties of interval extensions for non smooth functions are discussed. Then, selected formulas from [4] are presented. The formulas for slopes presented here represent improvements (sharper bounds) over those in [4] A simple, illustrative example is then given. Fourth, a convergence and existence uniqueness verification theory for interval Newton methods using non smooth extensions is developed. ....
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R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers, preprint, 1995.
Search Heuristics for Box Decomposition Methods - Ratschan (2003) (Correct)
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R. B. Kearfott. Interval extensions of non-smooth functions for global optimization and nonlinear systems solvers. Computing, 57(2):149--162, 1996.
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