E. R. Hansen and G. W. Walster. Nonlinear equations and optimization. Control and Games of Cornput. Math. Appl., 1991. To appear in the second special issue on Global Optimization. Home/Search Document Not in Database Summary Related Articles Check |
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Lifting Transformations - McAllester, Siskind (1991) (Correct)
....set. In the case of floating point lifting one may have to search for solutions to a system of nonlinear equations involving numerical variables. Our Common Lisp implementation of floating point lifting uses interval techniques to find solutions to systems of nonlinear equations [Hansen, 1968] [Hansen and Walster, 1991]. In the interval method one associates each numerical varialle with a numerical upper and lower hound. The two hounds define an interval of possible values for ech variable. New hounds can le inferred from existing hounds and constraints. For example, given the constraint : St 3.0) and an ....
.... This lifting transformation is appropriate for solving classical constraint satisfaction problems such as the eight queens puzzle, or line labeling problems in vision [Kirousis and Papadimitriou, 1988] van Hentenryck, 1989] McAllester, SThe interval method described in [Hansen, 1968] and [Hansen and Walster, 1991] apply to constraints on real numbers rather than to floating point representations. 14 1990] CSP lifting is described in the setting of the Common Lisp implementation in [Siskind and McAllester, 1992a] A variety of examples of constraint trans formed programs that run under our Common Lisp ....
E. R. Hansen and G. W. Walster. Nonlinear equations and optimization. Control and Games of Cornput. Math. Appl., 1991. To appear in the second special issue on Global Optimization.
Lifting - McAllester (1992) (Correct)
....variable a particular floating point value such that the resulting assignment is a solution to all constraints. It then returns the value of its argument. In the lifted implementation of the procedure LFLOAT FLOAT the constraints are solved using interval methods [Moore, 1966] Hansen, 1968] [Hansen and Walster, 1991]. The procedudure maintains upper and lower numerical bounds on each variable. It iteratively refines these bounds as follows. It selects x to be the LFLOAT variable with the largest the largest range of values, i.e. with the maximimum difference between the upper and lower bounds. If two ....
E. R. Hansen and G. W. Walster. Nonlinear equations and optimization. Control and Games of Comput. Math. Appl., 1991. To appear in the second special issue on Global Optimization.
Nondeterministic Lisp as a Substrate for Constraint Logic.. - Siskind, McAllester (1993) (21 citations) (Correct)
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E. R. Hansen and G. W. Walster. Nonlinear equations and optimization. Control and Games of Comput. Math. Appl., 1991. To appear in the second special issue on Global Optimization.
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