应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2012年
4期
360-367
,共8页
无约束最优化%拟牛顿法%Broyden-Fletcher-Goldfarb-Shanno%(BFGS)%修正拟牛顿法
無約束最優化%擬牛頓法%Broyden-Fletcher-Goldfarb-Shanno%(BFGS)%脩正擬牛頓法
무약속최우화%의우돈법%Broyden-Fletcher-Goldfarb-Shanno%(BFGS)%수정의우돈법
unconstrained optimization%quasi-Newton method%Broyden-Fletcher- Goldfarb-Shanno (BFGS)%modified quasi-Newton method
通过对函数的泰勒展开式进行误差分析, 提出了对二次模型进行改进的新模型, 在此基础上得到了改进的拟牛顿条件, 并得到了与其相应的Broyden-Fletcher-Goldfarb-Shanno （BFGS）算法. 证明了在适当条件下该算法全局收敛. 从试验函数库中选择标准测试函数, 对经典的BFGS算法与改进的BFGS算法进行数值试验, 试验结果表明改进的算法优于经典的BFGS算法.
通過對函數的泰勒展開式進行誤差分析, 提齣瞭對二次模型進行改進的新模型, 在此基礎上得到瞭改進的擬牛頓條件, 併得到瞭與其相應的Broyden-Fletcher-Goldfarb-Shanno （BFGS）算法. 證明瞭在適噹條件下該算法全跼收斂. 從試驗函數庫中選擇標準測試函數, 對經典的BFGS算法與改進的BFGS算法進行數值試驗, 試驗結果錶明改進的算法優于經典的BFGS算法.
통과대함수적태륵전개식진행오차분석, 제출료대이차모형진행개진적신모형, 재차기출상득도료개진적의우돈조건, 병득도료여기상응적Broyden-Fletcher-Goldfarb-Shanno （BFGS）산법. 증명료재괄당조건하해산법전국수렴. 종시험함수고중선택표준측시함수, 대경전적BFGS산법여개진적BFGS산법진행수치시험, 시험결과표명개진적산법우우경전적BFGS산법.
Based on the error analysis of the Taylor expansion, a new model for improving the quadratic model is put forward, and the new secant equation and the corresponding Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm are obtained. It is shown that under appropriate conditions, the algorithm is globally
convergent. Using the standard test function, the classic BFGS algorithm is compared to the modified BFGS algorithm in the numerical test. The experimental results show that the modified algorithm is better than the classic BFGS algorithm.
