The cluster problem in multivariate global optimization
نویسندگان
چکیده
منابع مشابه
The cluster problem in multivariate global optimization
We consider branch and bound methods for enclosing all unconstrained global minimizers of a nonconvex nonlinear twice-continuously differentiable objective function. In particular, we consider bounds obtained with interval arithmetic, with the “midpoint test,” but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undes...
متن کاملThe Cluster Problem in Global Optimization the Univariate Case
We consider a branch and bound method for enclosing all global minimizers of a nonlinear C2 or C1 objective function. In particular, we consider bounds obtained with interval arithmetic, along with the “midpoint test,” but no acceleration procedures. Unless the lower bound is exact, the algorithm without acceleration procedures in general gives an undesirable cluster of intervals around each mi...
متن کاملGlobal Optimization of Rational Multivariate Functions
The paper deals with unconstrained global minimization of rational functions. A necessary condition is given for the function to have a nite innmum. In case the condition is satissed, the problem is shown to be equivalent to a speciic constrained polynomial optimization problem. In this paper, we solve a relaxation of the latter formulation using semi-deenite programming. In general, the relaxa...
متن کاملThe Phase Problem: A Problem in Constrained Global Optimization
It is now almost 200 years since Gauss, a teenager at the time, formulated his famous principle of least-squares and used it to determine, for the first time, the orbit of one of the asteroids, a problem which had defeated astronomers for years. When applied to the crystallographic phase problem, least-squares leads directly to the formulation of the minimal principle, which effectively replace...
متن کاملPartical Swarm Optimization Applied To The Atomic Cluster Optimization Problem
The Particle Swarm Optimization method has proven quite successful in treating a variety of applied problems. Here we further test its capabilities by studying its behavior when applied to a challenging problem, namely the search for energy conformations of atomic clusters. In its simplest form this is known as the Lennard-Jones Problem. Results are compared with those achieved using simple Gen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Global Optimization
سال: 1994
ISSN: 0925-5001,1573-2916
DOI: 10.1007/bf01096455