On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications

Ning Ruan; David Yang Gao

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On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications

机译：关于具有应用程序的多尺度系统中一般定点问题的建模和完整解决方案

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This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e., the general fixed point problem is first reformulated as a nonconvex optimization problem, its well-posedness is discussed based on the objectivity principle in continuum physics; then the canonical duality theory is applied for solving this challenging problem to obtain not only all fixed points, but also their stability properties. Applications are illustrated by problems governed by nonconvex polynomial, exponential, and logarithmic operators. This paper shows that within the framework of the canonical duality theory, there is no difference between the fixed point problems and nonconvex analysis/optimization in multidisciplinary studies.

机译：本文从数学建模和典型对偶理论的统一角度重新研究了精心研究的不动点问题，即首先将一般不动点问题重构为非凸优化问题，并根据客观性原则讨论了它的适定性。连续物理然后将经典对偶理论用于解决这一难题，不仅获得所有固定点，而且获得其稳定性。由非凸多项式，指数和对数运算符控制的问题说明了应用程序。本文表明，在规范对偶理论的框架内，多学科研究中的定点问题和非凸分析/优化之间没有区别。

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《Fixexd point theory and applications》 |2018年第1期|共页
作者
Ning Ruan; David Yang Gao;
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中图分类数学;
关键词
47H1047H1455M0565K10Fixed pointProperly-posed problemNonconvex optimizationCanonical duality theoryMathematical modelingMultidisciplinary studies;

机译：47H1047H1455M0565K10定点正定问题非凸优化典型对偶理论数学建模多学科研究;

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On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications

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