Theory of index-one nonlinear complementarity systems
| Autor: | Peter Stechlinski |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Index (economics)
Applied Mathematics 010102 general mathematics Lexicographical order 01 natural sciences Implicit function theorem 010101 applied mathematics Orientation (vector space) Continuation Piecewise Applied mathematics Sensitivity (control systems) 0101 mathematics Analysis Mathematics Parametric statistics |
| Zdroj: | Journal of Differential Equations. 285:99-127 |
| ISSN: | 0022-0396 |
| DOI: | 10.1016/j.jde.2021.02.054 |
| Popis: | Generalized differentiation index-one nonlinear complementarity systems (NCSs) are mathematically regularized in this article. Strong regularity of solutions is shown to imply generalized differentiation index one holding, a concept from nonsmooth differential-algebraic equations (DAEs) theory. Well-posedness of NCSs is established, including continuation and maximal continuation of strongly-regular solutions. It is demonstrated that strongly-regular NCS solutions are lexicographically smooth (in the sense of Nesterov) with respect to parameters, implying Lipschitzian parametric dependence of solutions. These results are accomplished by relating strong regularity to complete coherent orientation from the theory of piecewise continuously differentiable functions, and an extended nonsmooth implicit function theorem useful for analyzing NCSs. The findings in this article lay the foundation for computationally-relevant sensitivity analysis theory and dynamic optimization methods for practical problems modeled using NCSs. Along the way, theory of semi-explicit DAEs with piecewise continuously differentiable right-hand side functions, which encompass a number of frameworks, is formalized. |
| Databáze: | OpenAIRE |
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