摘要
给出了一个求解正定二次规划的区域分解方法。首先证明了任何一个正定二次规划问题与一个有界区域上的正定二次规划问题是等价的。然后,依据一定的准则将有界区域分解成一系列的单纯形,通过求解每个单纯形上正定二次函数的最优解,迭代到原问题的最优解。该方法有很明显的优点:①求解单纯形上目标函数的最优解是一个无约束正定二次规划问题;②构造单纯形是通过求解线性规划问题得到。算例表明,本算法是有效的。
A region decomposition method to solve a positive definite quadratic programming is presented. It proved that any positive definite quadratic programming is equivalent to a positive definite quadratic programming in a boundary region. In the algorithm, the feasible region is decomposed into a series of simplice and iterating the optimal solutions in the simplice to the optimal solution of the original problem. There are some advantages : ① To find the minimum of a positive definite quadratic function in a simplex is equivalent to a non-constrained problem. ② The simplex is constructed by solving a linear problem. Numerical simulation shows that the method is feasible and can be used to solve the large-scale problems.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2003年第6期625-628,共4页
Journal of Northwest University（Natural Science Edition）
基金
航空科学基金资助项目(01J53079)
关键词
正定二次规划
单纯形
仿射流形
最优解
positive definite quadratic programming
simplex
affine manifold
optimal solution
