A Simple Multistart Algorithm for Global Optimization

1.IntroductionConsidertheunconstrainedoptimizationproblem:findx*suchthatf(x*)~caf(x),(1)wheref(x)isanonlinearfllnctiondefinedonW"andXCR".Ourobjectiveistofindtheglobalminimizeroff(x)inthefeasibleset.Withoutassuminganyconditionsonf(x)globaloptimizationproblemsareunsolvableinthefollowingsensefnoalgorithmcanbeguaranteedtofindaglobalminimizerofageneralnonlinearfunctionwithinfinitelymanyiterations.Supposethatanalgorithmappliedtoanonlinearfunctionf(x)producesiteratesxlandterminatesafterKiterations.…     

一类非线性算子的耦合不动点定理及其应用

本文定义了斜增算子及其耦合不动点，利用扩展算子的方法证明了斜增算子的耦合不动点定理，并给出了迭代公式。     

严格伪压缩映象的Ishikawa 迭代序列的收敛率估计

It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results.     

Type Numbers of Critical Points for Nonsmooth Functionals

Type numbers of critical points for Lipschitz functionals are studied. Versions of the Morse inequalities are established; it is shown that the topological index of an isolated critical point is equal to the alternated sum of its type numbers. Formulas for calculating the type numbers of the zero critical point of one functional are given.     

Topological dynamics of flipping Lorentz lattice gas models

We study the topological dynamics of the flipping mirror model of Ruijgrok and Cohen with one or an infinite number of particles. In particular we prove the topological transitivity and topological mixing up to a natural first integral for the one-particle model.     

On the structure of the set bases of a degenerate point

Consider an extreme point (EP)x ⁰ of a convex polyhedron defined by a set of linear inequalities. If the basic solution corresponding tox ⁰ is degenerate,x ⁰ is called a degenerate EP. Corresponding tox ⁰, there are several bases. We will characterize the set of all bases associated withx ⁰, denoted byB ⁰. The setB ⁰ can be divided into two classes, (i) boundary bases and (ii) interior bases. For eachB ⁰, there is a corresponding undirected graphG ⁰, in which there exists a tree which connects all the boundary bases. Some other properties are investigated, and open questions for further research are listed, such as the connection between the structure ofG ⁰ and cycling (e.g., in linear programs).     

Relative stability of f.c.c. and b.c.c. structures for model systems at high temperatures

Summary Free-energy, entropy and volume differences between face-centered and body-centered cubic structures have been evaluated for model rare gas and alkali metal crystals by using the method of overlapping distributions. Stable phases are predicted in agreement with the behaviour of real materials in the regions of validity of classical mechanics and in agreement with the results of previous dynamical-simulation studies of crystal nucleation from the melt and of polymorphic transformations. The existence of a stable b.c.c. phase at high pressure and temperatures is predicted in this way for Lennard-Jones solids, while no high-pressure f.c.c. phase is expected for model Rb and Cs systems. We also show the possibility of making calculations of free-energy barriers to displacive crystalline transformations along a prescribed trajectory in configuration space. Work supported by the U.S. Department of Energy, Istituto per la Ricerca Scientifica e Tecnologica, Trento, and Gruppo Nazionale di Struttura della Materia del C.N.R., Italy.     

Efficient spanning trees

The definition of a shortest spanning tree of a graph is generalized to that of an efficient spanning tree for graphs with vector weights, where the notion of optimality is of the Pareto type. An algorighm for obtaining all efficient spanning trees is presented.     

一类超椭圆曲线的整点个数

设ｎ是大于２的工整数，Ｄ是无平方因子正整数，分别是Ｋ的理想类群和类数．对于正整数ｍ，设ｇｋ（ｍ）是Ｉｘ中阶数等于ｍ的理想类的个数．本文证明了：超椭圆曲线ｆ（ｘ，ｙ）＝Ｄｘ２－４ｙｎ＋１＝０上整数点（ｘ，ｙ）的个数不超过ｍａｘ（８，２１６４Ｐ８１ｇｋ（Ｐ）），其中ｐ是ｎ的奇素因数．