Quadratic Convergence of a Newton Method for Nonlinear Programming

Abstract

A Newton algorithm for solving the problem minimize f(x) subject to g(x) - 0, where f:Rn - R and g:Rn - Rm is given for the case when g is concave. At each step a convex quadractic program with linear constraints is solved by means of a finite algorithm to obtain the next point. Quadratic convergence is established.