cd-regularity – 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)

ON REGULARITY CONDITIONS FOR COMPLEMENTARITY PROBLEMS

Published: 2012/02/28

Alexey F. Izmailov

A. S. Kurennoy

Complementarity and Variational Inequalities b-regularity, bd-regularity, cd-regularity, fischer-burmeister function, kkt system, mixed complementarity problem, natural residual function, nonlinear complementarity problems, quasi-regularity, semistability, strong regularity

In the context of mixed complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in related theoretical and algorithmic developments. In this note, we provide the complete picture of relations between the most important regularity conditions for mixed complementarity problems. A special attention is paid to the particular … Read more