GENERAL INFORMATION

We characterize the convex envelope of a given function f as the unique solution of a convex programming problem. It allows us to build a sequence of convex and polygonal function ^un that converges uniformly to the convex envelope of f.     

程序树层次化结构统计模型及MOSES改进算法

为提高MOSES效率,提出了一种新的程序树层次化结构统计模型.该模型通过统计分析同类群,自动发现子树特征来指导优化.该模型不需要hBOA算法那样对变量集合进行建模,也不需要像MRTS算法那样遍历小规模的种群来发现潜在的有指导意义的子树.通过解决人工蚂蚁问题对算法进行了测试,结果表明改进后的MOSES算法更加高效.     

模糊线性规划的对称曲边岭形模型

用扩张原理，对模糊线性规划中参数为对称等腰岭形的情形建立了相应的模型化公式，并把这类问题转化为非线性规划求解     

Some Results on Mathematical Programming with Generalized Ratio Invexity

In this paper, a generalized ratio invexity concept has been applied for single objective fractional programming problems. A concept which has been invoked seems to be more general than the one used earlier by Khan and Hanson in such contexts. Further, duality results for fractional programs have also been obtained.     

不确定性结构的弹塑性分析：模型及其解法

本文处理一类重要的工程问题：不确定性结构的弹塑性分析，分析模型包含了一类分片线性的硬化法则，这包含了大范围实际观察所得的材料特性。我们所处理的不确定性是由荷载及材料参数引起的。本文先把问题转化为一个随机非线性规划问题，然后用逼近技术给出一个简单的求解方法。     

Testing optimality for quadratic 0-1 problems

Received June 4, 1996 / Revised version received November 19, 1997 Published online November 24, 1998     

A branch-and-cut method for 0-1 mixed convex programming

We generalize the disjunctive approach of Balas, Ceria, and Cornuéjols [2] and devevlop a branch-and-cut method for solving 0-1 convex programming problems. We show that cuts can be generated by solving a single convex program. We show how to construct regions similar to those of Sherali and Adams [20] and Lovász and Schrijver [12] for the convex case. Finally, we give some preliminary computational results for our method. Received January 16, 1996 / Revised version received April 23, 1999?Published online June 28, 1999     

数学双语教学的几点思考

双语教学是现代高等教育教学改革的重点之一,是培养具有国际合作意识、国际交流与竞争能力的国际型人才的重要途径。结合中英合作班数学双语教学情况,从教学目的,授课方式,教材建设等方面阐述了笔者在双语教学过程中的一些实践经验。     

关于一例数学建模竞赛题假设合理性的研究

对2001年全国大学生数学建模竞赛C题参考答案的假设中的“奖金在年底发放”提出了异议，认为该假设只是使奖金额达到最大，但方案的可操作性很弱，不符合实际情况．给出了新的符合实际的假设一每年1月1日预留当年奖金，奖金可在一年中任何时候发放，并根据新的假设对C题重新建立了数学模型，得到了新的投资方案．     

Designing an optimal connected nature reserve

We consider a landscape divided into elementary cells, each of these cells containing some species to be protected. We search to select a set of cells to form a natural reserve in order to protect all the species present in the landscape. A species is considered protected if it is present in a certain number of cells of the reserve. There is an important spatial constraint concerning the set of selected cells: a species must be able to go from any cell to any cell without leaving the reserve. An integer linear programming model was proposed by Önal and Briers [2] for this reserve selection problem, but the size of the problems which can be handled by this model is limited: several hours of computation are required for solving instances with hundred of cells and hundred of species. Having proposed an improvement of this model which reduces appreciably the computation time, we propose another integer linear programming model, easy to carry out, which allows to obtain, in a few seconds of computation, optimal or near-optimal solutions for instances with hundred of cells and hundred of species. However, the computation time becomes prohibitive for instances with more than 200 cells and 100 species. But, this approach can be particularly useful to solve the problem, in an approximate way, by aggregation of cells as proposed by Önal and Briers [2].