Solving convex quadratic programming by potential-reduction interior-point algorithm

The solution of quadratic programming problems is an important issue in the field of mathematical programming and industrial applications. In this paper, we solve convex quadratic programming by a potential-reduction interior—point algorithm. It is proved that the potential—reduction interior-point algorithm is globally convergent. Some numerical experiments were made.     

以杆长平方和为目标函数进行形状优化的二次规划方法

给出了桁架结构形状优化的一种分层方法，即分为截面层优化和节点层优化．在节点层，不以结构的重量作为目标函数，而以杆长平方和作为目标函数，形成了标准的二次规划，采用Ｌｅｍｋｅ方法即可求解．     

凸二次规划问题基于核函数的全牛顿步内点算法

针对凸二次规划问题,构造了新的核函数.通过构造的核函数来确定搜索方向和逼近度量,接着给出了求解凸二次规划问题的全牛顿步内点算法,最后给出了算法的复杂性界.     

非线性凸半定规划的割平面算法

先把一般的非线性凸半定规划转化成目标函数是线性函数的非线性凸半定规划,然后用割平面算法求解转化后的半定规划．最后证明了割平面算法的收敛性．     

基于对数变换的凸二次规划不可行内点算法

基于对数变换和不可行内点算法,对凸二次规划提出了一种新的迭代方向原始-对偶不可行内点算法,并证明了算法的全局收敛性和多项式复杂性,该算法可以看做近期Pan等人关于线性规划算法的推广.     

Global optimality conditions for quadratic 0–1 programming with inequality constraints

Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.     

一类下降的谱共轭梯度法

在标准DY共轭梯度法和谱FR共轭梯度法的基础上，讨论一类满足βk=gTkdkgTk-1dk-1性质的谱共轭梯度法，在Wolfe线搜索条件下算法具有下降性和全局收敛性，初步的数值实验结果表明该方法是有效的，适合于求解非线性无约束优化问题。