Pure adaptive search in monte carlo optimization

Pure adaptive search constructs a sequence of points uniformly distributed within a corresponding sequence of nested regions of the feasible space. At any stage, the next point in the sequence is chosen uniformly distributed over the region of feasible space containing all points that are equal or superior in value to the previous points in the sequence. We show that for convex programs the number of iterations required to achieve a given accuracy of solution increases at most linearly in the dimension of the problem. This compares to exponential growth in iterations required for pure random search.     

两类拟共形映射的掩盖定理

In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.     

A result on sets,with applications to vector optimization

In this paper there is stated a result on sets in ordered linear spaces which can be used to show that some properties of the sets are inherited by their convex hulls under suitable conditions. As applications one gives a characterization of weakly efficient points and a duality result for nonconvex vector optimization problems.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

近严格凸与最佳逼近

本文研究近严格凸与最佳逼近的关系．证明了Ｂａｎａｃｈ空间Ｘ是近严格凸的当且仅当Ｘ的每个子空间是紧－半－切比晓夫空间．     

Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices

The sum of the largest eigenvalues of a symmetric matrix is a nonsmooth convex function of the matrix elements. Max characterizations for this sum are established, giving a concise characterization of the subdifferential in terms of a dual matrix. This leads to a very useful characterization of the generalized gradient of the following convex composite function: the sum of the largest eigenvalues of a smooth symmetric matrix-valued function of a set of real parameters. The dual matrix provides the information required to either verify first-order optimality conditions at a point or to generate a descent direction for the eigenvalue sum from that point, splitting a multiple eigenvalue if necessary. Connections with the classical literature on sums of eigenvalues and eigenvalue perturbation theory are discussed. Sums of the largest eigenvalues in the absolute value sense are also addressed.This paper is dedicated to Phil Wolfe on the occasion of his 65th birthday.The work of this author was supported by the National Science Foundation under grants CCR-8802408 and CCR-9101640.The work of this author was supported in part during a visit to Argonne National Laboratory by the Applied Mathematical Sciences subprogram of the Office of Energy Research of the U.S. Department of Energy under contract W-31-109-Eng-38, and in part during a visit to the Courant Institute by the U.S. Department of Energy under Contract DEFG0288ER25053.     

凸集的广义Reuleaux三角形

常宽凸集的面积最小者为Reulaux三角形，而非常宽凸集的面积最小者为何呢？它就是本文将给出的广义Reuleaux三角形△R。     

Banach空间中凸映照的增长定理

本文利用凸映照的几何特征证明了一般复Banach空间中单位球上正规化双全纯凸映照的增长定理，即||f(x)||≤||x||/(1-||x||),A↓x∈B，对复内积空间，上述估计是最佳的。     

Differential subordinations concerning starlike functions

Denote byS ^* (⌕), (0≤⌕<1), the family consisting of functionsf(z)=z+a ₂z²+...+a_nzⁿ+... that are analytic and starlike of order ⌕, in the unit disc ⋎z⋎<1. In the present article among other things, with very simple conditions on μ, ⌕ andh(z) we prove the f’(z) (f(z)/z)^μ−1<h(z) implies f∈S^*(⌕). Our results in this direction then admit new applications in the study of univalent functions. In many cases these results considerably extend the earlier works of Miller and Mocanu [6] and others.     

球约束凸二次规划的一个新算法

首先利用Lagrange对偶 ,将球约束凸二次规划问题转化为无约束优化问题 ,然后运用单纯形法求解无约束优化问题 ,从而获得原问题的最优解