不等式约束最优化无严格互补条件下的快速收敛序列线性方程组算法  

A Fast Convergent Algorithm of Sequential Systems of Linear Equations for Inequality Constraind Optimization without Strict Complementarity

作　　者：简金宝[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《数学学报（中文版）》2004年第4期781-792,共12页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10261001);广西自然科学基金(0236001;0249003)

摘　　要：本文讨论无严格互补性的非线性不等式约束最优化问题,建立了一个新的序列线性方程组算法。算法每次迭代只需解一个线性方程组或计算一次广义梯度投影,并不要求Lagrange函数的近似Hessian阵正定。在较弱的假设下,证明了算法的整体收敛性、强收敛性、超线性收敛性及二次收敛速度。还对算法进行了有效的数值试验。In this paper, the nonlinear inequality constrained optimization problems without the strict complementarity condition are discussed, and a new algorithm of se- quential systems of linear equations (i.e. SSLE) for the problems is proposed. At each iteration, the algorithm solves only one system of linear equations or computes a gen- eralized gradient projection, where the approximate Hessian of the Lagrange function is not necessary positive definite. Under weaker coditions, we prove that the algo- rithm possesses global, strong, and supperlinear convergence, and a rate of quadratic convergence. Some efficieat numerical experiments are given.

关 键 词：不等式约束 非线性最优化 序列线性方程组 

分 类 号：O221.2[理学—运筹学与控制论]