An Approach to Homotopy and Degree Theory
An Approach to Homotopy and Degree Theory
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DOI：
10.1287/moor.4.4.390
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发表时间：
1979-11
期刊：
影响因子：
--
通讯作者：
C. B. García;W. Zangwill
中科院分区：
文献类型：
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作者：
C. B. García;W. Zangwill
斯卡夫在定点计算方面的开创性工作催生了数学规划的一个全新领域。许多可以表现为不动点问题的问题，例如涉及平衡、博弈、方程组、全局优化和结构力学的问题，都已进入这些新的构造性技术的范围。这些技术的基础是来自微分拓扑的某些数学概念，更具体地说是布劳威尔度理论和同伦。通常，这些概念所需的数学机制需要非常熟悉分段线性和/或微分拓扑。在本文中，沿着常微分方程产生的路径进行发展。微分方程由线性方程的克拉默规则得出。我们的方法的适用性和易用性通过获得微分拓扑定理的简单证明来证明。
Spawned by Scarf's pioneering work on the calculation of fixed points, an entire new field in mathematical programming has emerged. A wide array of problems that can be posed as fixed point problems, such as problems involving equilibria, games, systems of equations, global optimization, and structural mechanics, have come into the purview of these new constructive techniques. Underlying these techniques are certain mathematical concepts from differential topology, more specifically degree theory Brouwer and homotopies. Usually, the mathematical machinery required for these concepts necessitates a keen familiarity with piecewise linear and/or differential topology. In this paper, the development is made by following the paths arising from an ordinary differential equation. The differential equation results from Cramer's rule for linear equations. The applicability and ease of our approach are shown by obtaining simple proofs of theorems in differential topology.