local convergence theorem 中文意思是什麼
local convergence theorem
解釋
局部收斂定理- local : adj 1 地方的，當地的，本地的。2 局部的。3 鄉土的，狹隘的，片面的。4 【郵政】本市的，本地的；【鐵...
- convergence : n. 1. 聚合，會聚，輻輳，匯合。2. 集合點；【數、物】收斂；【生物學】趨同（現象）。
- theorem : n. 1. （能證明的）一般原理，公理，定律，法則。2. 【數學】定理。
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It is proven that these modified dual algorithms still have the same convergence results as those of the conceptional dual algorithms in chapter 2 and chapter 3. secondly, a dual algorithm is constructed for general constrained nonlinear programming problems and the local convergence theorem is established accordingly. the condition number of modified lagrange function ' s hessian is estimated, which also depends on the penalty parameter
證明這些修正的對偶演算法仍具有同前兩章的概念性對偶演算法相同的收斂性結果，我們還進一步構造了一般約束非線性規劃問題的對偶演算法，建立了相應的局部收斂理論，最後估計了修正lagrange函數的hesse陣的條件數，它同樣依賴于罰參數。 -
The local convergence theorem is important because it shows the property of the iterative method near the solution, but the shortcoming is that its codition depends on the unknown solution
局部收斂性定理固然很重要，因為它不僅提供了一個關于收斂性的結果，而且還表徵著某些迭代過程在一個解的鄰域內的理論性態。 -
In the nineteenth century, when researchers began to pay attention to the analysis strictness in mathematics, cauchy put forward major series technique, which was confirmed highly effective in applying it to the convergence analysis of iterations. there are three kinds of convergence theorems which related to iterative method, a ) local convergence theorem, b ) semilocal convergence theorem, c ) global convergence theorem
對于迭代法收斂性的研究，數值工作者們做了大量的工作（見文後的參考文獻） ，但我們知道與迭代過程相關的收斂性定理通常有三種類型： a ）局部的； b ）半局部的； c ）全局的或整體的收斂性定理。 -
Chapter 2 establishes the theoretical framework of a class of dual algorithms for solving nonlinear optimization problems with inequality constraints. we prove, under some mild assumptions, the local convergence theorem for this class of dual algorithms and present the error bound for approximate solutions. the modified barrier function methods of polyak ( 1992 ) and the augmented lagrange function method of bertsekas ( 1982 ) are verified to be the special cases of the class of dual algorithms
第2章建立求解不等式約束優化問題的一類對偶演算法的理論框架，在適當的假設條件下，證明了該類演算法的局部收斂性質，並給出近似解的誤差界，驗證了polyak （ 1992 ）的修正障礙函數演算法以及bertsekas （ 1982 ）的增廣lagrange函數演算法都是這類演算法的特例。
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