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A special Newton-type optimization method. (English) Zbl 0814.65063
Summary: 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.

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
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