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 ...

Abstract: This paper is a survey of some results on Newton's method as applied to the implicit function theorem, homotopy methods, and Bezout's theorem. An application to macroeconomics is also ...

Abstract: 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 ...