Continuous second order minimization method with variable metric projection operator

Variable Metric Method for Minimization

Variable metric method for minimization of partially separable nonsmooth functions

In this report, we propose a new partitioned variable metric method for minimizing nonsmooth partially separable functions. After a short introduction, the complete algorithm is introduced and some implementation details are given. We prove that this algorithm is globally convergent under standard mild assumptions. Computational experiments given confirm efficiency and robustness of the new met...

On Stability of the Metric Projection Operator

Abstract. Let M be a closed linear subspace of a normed linear space X. For a given f ∈ X denote by PM f the set of best approximations to f from M . The operator PM is termed the metric projection onto M . In this paper we are interested in the stability of the metric projection PM relative to perturbations of the subspace M . We mainly consider the case where X = Lp, p ∈ [1,∞]. We consider a ...

A Nonmonotone Second - Order Steplength Method for Unconstrained Minimization

In this paper, a nonmonotone method based on McCormick’s second-order Armijo’s step-size rule [7] for unconstrained optimization problems is proposed. Every limit point of the sequence generated by using this procedure is proved to be a stationary point with the second-order optimality conditions. Numerical tests on a set of standard test problems are presented and show that the new algorithm i...

Computational experience with improved variable metric methods for unconstrained minimization

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library The paper describes ...