几何规划的广义梯度投影内点算法  

Generalized Gradient Projection Interior Point Algorithm for Geometric Programming

作　　者：党亚峥[1,2] 景书杰[2] 张可村[3] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]河南理工大学数学与信息科学学院,焦作454001 [3]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2009年第3期461-465,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金重点资助项目(10671057);河南理工大学青年基金(Q2009-3)

摘　　要：本文首先利用对偶理论将正定式几何规划转化为带有非负约束和线性等式约束下的一般非线性规划问题;其次将广义梯度投影算法与内点算法相结合构造出了广义梯度投影内点算法来求解这个非线性规划问题;最后进一步证明了这种算法的收敛性质。此算法不需要计算与跟踪主动约束集,减少了计算量。In this paper, we firstly change the postive-type geometric-programming into the usual nonliner programming by making use of the dual theory; by integrating the general gradient-projection algorithm and the interior-point algorithm, a new algorithm is derived to solve the nonliner program- ming; last, we prove the convergence of the designed algorithm. The algorithm does not need to know and track the active constraint set, which reduces its complexity.

关 键 词：几何规划 对偶规划 梯度投影算法 内点算法 

分 类 号：O224[理学—运筹学与控制论]