Iterated Hamiltonian type systems and applications
Iterated Hamiltonian type systems and applications
复制标题
迭代哈密顿类型系统和应用
DOI：
10.1016/j.jde.2018.01.003
复制
发表时间：
2018
影响因子：
2.4
通讯作者：
D. Tiba
中科院分区：
文献类型：
--
作者：
D. Tiba
本文介绍了一种构造性方法，通过哈密顿型方程给出了任意维一般隐式系统的局部解。这种方法的一个变体构造流形的参数化，扩展了通常的隐函数解决方案。我们还讨论了隐函数定理的临界情形，定义了广义解的概念，证明了广义解的存在性和性质。并举例说明。应用涉及非凸优化问题及其扰动的必要条件和算法。
We introduce a constructive method that provides the local solution of general implicit systems in arbitrary dimension via Hamiltonian type equations. A variant of this approach constructs parametrizations of the manifold, extending the usual implicit functions solution. We also discuss the critical case of the implicit functions theorem, define the notion of generalized solution and prove existence and properties. Examples are also indicated. The applications concern necessary conditions and algorithms in nonconvex optimization problems and their perturbations.