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Metody s proměnnou metrikou s omezenou pamětí, založené na invariantních maticích
Vlček, Jan ; Lukšan, Ladislav
A new class of limited-memory variable metric methods for unconstrained minimization is described. Approximations of inverses of Hessian matrices are based on matrices which are invariant with respect to a linear transformation. As these matrices are singular, they are adjusted for a computation of direction vectors. The methods have the quadratic termination property, which means that they will find a minimum of a strict quadratic function with an exact choice of a step-length after a finite number of steps. Numerical experiments show the efficiency of this method.
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Shifted Variable Metric Methods for Unconstrained Optimization
Lukšan, Ladislav ; Vlček, Jan
A family of shifted variable metric methods for unconstrained optimization is investigated. These methods form a basis for shifted limited-memory variable metric methods introduced in second contribution in proceedings of SANM 2003. We describe basic properties of these methods, establish their global convergence and give conditions for the superlinear rate of convergence. Their efficiency is demonstrated by using extensive numerical experiments.
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