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It is shown that the rate of convergence in the von Mises conditions of extreme value theory determines the distance of the underlying distribution function F from a generalized Pareto distribution. The distance is measured in terms of the pertaining densities with the limit being ultimately attained if and only if F is ultimately a generalized Pareto distribution. Consequently, the rate of convergence of the extremes in an lid sample, whether in terms of the distribution of the largest order statistics or of corresponding empirical truncated point processes, is determined by the rate of convergence in the von Mises condition. We prove that the converse is also true.
In this paper, convex approximation methods, suclt as CONLIN, the method of moving asymptotes (MMA) and a stabilized version of MMA (Sequential Convex Programming), are discussed with respect to their convergence behaviour. In an extensive numerical study they are :finally compared with other well-known optimization methods at 72 examples of sizing problems.
In distance geometry problems and many other applications, we are faced with the optimization of high-dimensional quadratic functions subject to linear equality constraints. A new approach is presented that projects the constraints, preserving sparsity properties of the original quadratic form such that well-known preconditioning techniques for the conjugate gradient method remain applicable. Very-largescale cell placement problems in chip design have been solved successfully with diagonal and incomplete Cholesky preconditioning. Numerical results produced by a FORTRAN 77 program illustrate the good behaviour of the algorithm.