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Attraction of Newton method to critical Lagrange multipliers: fully quadratic case

A.F. Izmailov(izmaf***at***ccas.ru)
E.I. Uskov(ydoom***at***narod.ru)

Abstract: All previously known results concerned with attraction of Newton-type iterations for optimality systems to critical Lagrange multipliers were a posteriori by nature: they were showing that in case of convergence, the dual limit is in a sense unlikely to be noncritical. This paper suggests the first a priori result in this direction, showing that critical multipliers actually serve as attractors: for a fully quadratic optimization problem with equality constraints, under certain reasonable assumptions we establish actual local convergence to a critical multiplier starting from a “dense” set around the given critical multiplier. This is an important step forward in understanding the attraction phenomenon.

Keywords: quadratic optimization problem, Lagrange optimality system, critical Lagrange multiplier, Newton method.

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation: Moscow State University, OR Department, 2012

Download: [PDF]

Entry Submitted: 02/07/2013
Entry Accepted: 02/07/2013
Entry Last Modified: 02/07/2013

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