This paper concerns a derivation of second-order necessary conditions for a fixed-endpoint control problem of Lagrange involving mixed equality and/or inequality constraints, posed over piecewise ...

In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of coordinates ...

Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...

A collection of advanced autodiff primitive rules that built upon the implicit function theorem both for discrete problems (like solving linear systems of equations) and (semi-)continuous problems ...

At the positive equilibrium point, we demonstrate that the system’s unique positive equilibrium is globally asymptotically stable by using the Dulac criterion. Furthermore, at this equilibrium point, ...

Kharlamapovich, O. and Myasnikov, A. (2005) The Implicit Function Theorem over Free groups. Journal of Algebra, 290, 1-203.