天津师范大学学报（自然科学版）
天津師範大學學報（自然科學版）
천진사범대학학보（자연과학판）
JOURNAL OF TIANJIN NORMAL UNIVERSITY(NATURAL SCIENCE EDITION)
2009年
3期
18-21
,共4页
等式约束非线性规划%投影Hessian矩阵算法%超线性收敛
等式約束非線性規劃%投影Hessian矩陣算法%超線性收斂
등식약속비선성규화%투영Hessian구진산법%초선성수렴
nonlinear programming with equality constraint%projection method with Hessian matrix%superlinear convergence
分析了求解等式约束非线性规划问题的投影Hessian矩阵算法,找出了算法两步Q超线性收敛的原因,并用BYRD的例子说明此算法的收敛效果较差,即甚至不是线性收敛;对算法进行了合理的改进,并用改进后的算法求解BYRD问题,得到了满意的收敛效果,即Q超线性收敛.借助数值试验验证了改进算法的快速收敛性.
分析瞭求解等式約束非線性規劃問題的投影Hessian矩陣算法,找齣瞭算法兩步Q超線性收斂的原因,併用BYRD的例子說明此算法的收斂效果較差,即甚至不是線性收斂;對算法進行瞭閤理的改進,併用改進後的算法求解BYRD問題,得到瞭滿意的收斂效果,即Q超線性收斂.藉助數值試驗驗證瞭改進算法的快速收斂性.
분석료구해등식약속비선성규화문제적투영Hessian구진산법,조출료산법량보Q초선성수렴적원인,병용BYRD적례자설명차산법적수렴효과교차,즉심지불시선성수렴;대산법진행료합리적개진,병용개진후적산법구해BYRD문제,득도료만의적수렴효과,즉Q초선성수렴.차조수치시험험증료개진산법적쾌속수렴성.
The projection method with Hessian matrix used to solve nonlinear programming with equality constraint is analyzed and the reason why the method is superlinear convergent by two steps is found out. Its bad convergent effect at linearity is illuminated by BYRDs example. The method is improved and quickly superlinear convergence of the improved method is illuminated using BYRDs example. The quickly convergent effect of the improved method is verified by a numerical experiment.
