本文選題：優(yōu)化方法 + 切線交點法　； 參考：《機械設(shè)計與研究》2017年02期

【摘要】：優(yōu)化方法由數(shù)學(xué)推演的運用而體現(xiàn)其理論性。牛頓法是理論性最強的一維優(yōu)化方法,也稱為二階近似式法或?qū)Ш瘮?shù)切線零點法。類比該方法,以目標函數(shù)切線為出發(fā)點提出了目標函數(shù)切線交點法。采用一定的方法確定導(dǎo)數(shù)符號相反的相鄰兩點,在目標函數(shù)曲線上,在對應(yīng)于該兩點處分別做切線,其切線傾斜方向相反,將兩條切線平移到表示設(shè)計變量的數(shù)軸上,令兩條切線的交點對應(yīng)于新點;在三點中確定導(dǎo)數(shù)符號相反的相鄰兩點重復(fù)上述運算,直到滿足終止條件為止。算例證明,切線交點法的尋優(yōu)效果比對稱等比例區(qū)間削去法(黃金分割法)的好,并且可解決牛頓法難以解決的優(yōu)化問題。
[Abstract]:The optimization method embodies its theory by the application of mathematical deduction. Newton method is the most theoretical one-dimensional optimization method, also known as the second order approximation method or derivative tangent zero point method. By analogy with this method, the tangent point method of objective function is put forward with tangent of objective function as the starting point. Two adjacent points with opposite derivative symbols are determined by a certain method. On the objective function curve, tangent lines are made at the corresponding two points, and the tangent tilting direction is opposite, and the two tangent lines are moved to the number axis representing the design variable. Let the intersection of two tangent lines correspond to the new point, and repeat the above operations at the adjacent two points in which the derivative sign is opposite, until the termination condition is satisfied. The example shows that the tangent intersection method is better than the symmetric equal proportion interval cutting method (golden section method) and can solve the optimization problem which is difficult to be solved by Newton method.
【作者單位】： 中國石油大學(xué)(華東)中國石油大學(xué)勝利學(xué)院;東營市勝利第二中學(xué);東營市勝利第三中學(xué);
【基金】：山東省自然科學(xué)基金資助項目(Q2006A08)
【分類號】：O224

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