Séance Séminaire

Séminaire ACSIOM

Variational Analysis and its applications in engineering

This talk is devoted to the study of the Aubin/Lipschitz-like property and the isolated calmness of a particular non-monotone generalized equation arising in electrical engineering. The variational and non-smooth analysis is applied in the theory of non-regular electrical circuits involving electronic devices like ideal diodes, practical diodes, DIACs, silicon controlled rectifiers (SCR), and transistors. We also discuss the relationship of our results to the ones using classical techniques from (smooth) analysis and provide a simulation for several simple electrical circuits which are chosen in order to cover the most common non-smooth elements in electronics. We present also some results on stability of both local and global metric regularity under set-valued perturbations. As an application, we study (super-)linear convergence of the Newton-type iterative process for solving generalized equations. The possibility to choose set-valued approximations allows us to describe several iterative schemes in a unified way (such as inexact Newton method, non-smooth Newton method for semi-smooth functions, inexact proximal point algorithm, etc.).