Solvability and convergence of iterative algorithms for certain functional equations arising in dynamic programming

被引：8

作者：

Liu, Zeqing ^{[1
]}

Kang, Shin Min ^{[2
,3
]}

Ume, Jeong Sheok ^{[4
]}

机构：

[1] Liaoning Normal Univ, Dept Math, Dalian 116029, Liaoning, Peoples R China

[2] Gyeongsang Natl Univ, Dept Math, Jinju 660701, South Korea

[3] Gyeongsang Natl Univ, Res Inst Nat Sci, Jinju 660701, South Korea

[4] Changwon Natl Univ, Dept Appl Math, Chang Won 641773, South Korea

来源：

OPTIMIZATION | 2010年 / 59卷 / 06期

关键词：

dynamic programming; functional equation; solution; nonpositive solution; nonnegative solution; nonexpansive mapping; Banach fixed-point theorem; iterative algorithm; EXISTENCE THEOREMS;

D O I：

10.1080/02331930902884182

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this article, we introduce and study the following functional equation arising in dynamic programming of multistage decision processes: [image omitted] In order to solve the functional equation, we suggest some iterative algorithms. Under certain conditions we give a few sufficient conditions ensuring both the existence and uniqueness of solution for the functional equation and the convergence of these iterative algorithms with respect to the solution. We investigate also properties of nonpositive solutions and nonnegative solutions for several functional equations which are special cases of the above mentioned functional equation. To illustrate the results presented in this article, we construct eight nontrivial examples.

引用

页码：887 / 916

页数：30