Constant rank constraint qualifications - a geometric introduction

Roberto Andreani and Paulo J. S. Silva. Pesquisa Operacional, 2014.

Abstract

Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assump- tions that ensure that the polar of the linear approximation of the tangent cone, generated by the active gradients, retains it geometric structure locally.