A special newton-type optimization method

Abstract

Abstract The Kuhn–Tucker conditions of an optimization problem with inequality constraints are transformed equivalently into a special nonlinear system of equations T 0(z) = 0. It is shown that Newton's method for solving this system combines two valuable properties: The local Q-quadratic convergence without assuming the strict complementary slackness condition and the regularity of the Jacobian of T 0 at a point z under reasonable conditions, so that Newton's method can be used also far from a Kuhn–Tucker point Keywords: Nonlinear Programming AlgorithmsInequality ConstraintsKuhn-Tucker PointsNewton's MethodClarke's JacobianStrict Complementary Slackness Condition