An algorithm is proposed for the minimization of a smooth function subject to smooth
inequality constraints. Unlike sequential quadratic programming type methods, this
algorithm does not involve the solution of quadratic programs, but merely that of linear
systems of equations. Locally the iteration can be viewed as a perturbation of a quasi-
Newton iteration on both the primal and dual variables for the solution of the equalities in the
Kuhn-Tucker first order conditions of optimality. It is observed that, provided the current …

In this paper, we propose a new QP-free method, which ensures the feasibility of all iterates,
for inequality constrained optimization. The method is based on a nonsmooth equation
reformulation of the KKT optimality condition, by using the Fischer--Burmeister nonlinear
complementarity problem function. The study is strongly motivated by recent successful
applications of this function to the complementarity problem and the variational inequality
problem. The method we propose here enjoys some advantages over similar methods …