Showing papers on "Auxiliary function published in 1992"
TL;DR: In this article, the authors describe the numerical analysis of continuous univariate probability functions with S-systems, which are computationally efficient nonlinear ordinary differential equations that contain virtually all ordinary differential equation as special cases.
Abstract: This tutorial describes the numerical analysis of continuous univariate probability functions with S-systems. These are computationally efficient nonlinear ordinary differential equations that contain virtually all ordinary differential equations as special cases. After a brief introduction to S-systems, it is shown how central and noncentral probability distributions, as well as auxiliary functions such as Bessel, Gamma, and Beta functions, can be recast equivalently as S-systems. The representation of distributions as S-systems permits rapid computation of function evaluations over wide ranges of random variables, as well as moments, quantiles, power and inverse power. It also offers transformation methods and various options of approximation. The recasting procedure employs elementary mathematics and needs to be executed only once. The tutorial contains a catalogue of recast S-system representations for nearly all relevant distributions and auxiliary functions, and thus enables the reader to evaluate d...
18 citations
01 Jan 1992
TL;DR: Two classes of EAP are presented for a nonlinear programming problem without assumption that the problem has a saddle point of Lagrange function.
Abstract: A function is said to be on exact auxiliary function (EAP). if the set of global minimizers of this function coincides with the global solution set of initial optimization problem. Sufficient conditions for exact equivalence of constrained minimization problem and minimization of EAP are provided. Paper presents two classes of EAP for a nonlinear programming problem without assumption that the problem has a saddle point of Lagrange function.
5 citations
TL;DR: The problem of classifying a critical stationary point of a given objective function is reduced to the application of higher-order optimality conditions for a special auxiliary function.
Abstract: A stationary point of an unconstrained optimization problem is called critical if the Hessian matrix at this point is positive semidefinite. Such a point cannot be classified using second-order optimality conditions. In this paper the problem of classifying a critical stationary point of a given objective function is reduced to the application of higher-order optimality conditions for a special auxiliary function.
4 citations