Attraction of Newton method to critical Lagrange multipliers: fully quadratic case
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
Entry Submitted: 02/07/2013
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