解二次规划的Lagrange方法

本文讨论解二次规划问题的 Lagrange 方法。我们分析了解正定二次规划和某些半正定二次规划的对偶算法,指出这些算法可以从 Lagrange 方法直接导出。此外我们还给岀了解不定二次规划的一个新的 Lagrange 算法。这一算法在投影矩阵为不定矩阵时,利用广义的 Cholesky 分解技术由 Lagrange 方程解得二次目标函数的负曲率方向,以此作为该步迭代寻查方向。算法还采用了有效集策略。

LAGRANGIAN METHODS FOR SOLVING QUADRATIC PROGRAMMING PROBLEM

In this paper we are interested in the Lagrangian methods for solving quadratic programming prohlem.We analyse the dual algorithms for positive dofinite and certain semi-positive definite quadratic programming and in- dicate that these algorithms can be derived from the Lagrangian methods.Be- sides,we present a new algorithm in which,when the projective matrix is indefinite,we can solve a Lagrange eqtuakion by using generalized Cholesky factorization to get the negative curvature direction of the objective function. The active set strategy is also adopted in the algorithm.