A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions
Giorgio Giorgi · RePEc: Research Papers in Economics · 2018
It is well-known that the celebrated Kuhn-Tucker or Karush-Kuhn-Tucker necessary optimality conditions hold at a local solution point of a nonlinear programming problem if some regularity conditions, usually called "constraint qualifcations", are satisfied. In the present paper we give an up-to-date overview of several constraint quali?cations proposed in the literature for a nonlinear programming problem, under differentiability assumptions. In particular, we point out the various implications existing among the constraint qualifications considered. For the reader's convenience we shall consider separately the case of inequality constraints only and the case of mixed equality and inequality constraints. Some remarks on second-order constraint qualifications are made and some historical notes on this subject are given.