implicit function theorem – Optimization Online

STRONGLY REGULAR NONSMOOTH GENERALIZED EQUATIONS (REVISED)

Published: 2012/07/03, Updated: 2015/02/18

Complementarity and Variational Inequalities cd-regularity, generalized equation, generalized jacobian, implicit function theorem, inverse function theorem, strong regularity

This note suggests the implicit function theorem for generalized equations, unifying Robinson’s theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings. Article Download View STRONGLY REGULAR NONSMOOTH GENERALIZED EQUATIONS (REVISED)

DIRECT SEARCH METHODS OVER LIPSCHITZ MANIFOLDS

Published: 2007/08/02

David W. Dreisigmeyer

Constrained Nonlinear Optimization direct search, implicit function theorem, inverse function theorem, lipschitz manifold, ltmads

We extend direct search methods to optimization problems that include equality constraints given by Lipschitz functions. The equality constraints are assumed to implicitly define a Lipschitz manifold. Numerically implementing the inverse (implicit) function theorem allows us to define a new problem on the tangent spaces of the manifold. We can then use a direct search … Read more