scholarly journals Complexity bounds for second-order optimality in unconstrained optimization

2012 ◽  
Vol 28 (1) ◽  
pp. 93-108 ◽  
Author(s):  
C. Cartis ◽  
N.I.M. Gould ◽  
Ph.L. Toint
Keyword(s):  
Unconstrained Optimization ◽  
Second Order ◽  
Complexity Bounds

scholarly journals An algorithm for LC1 optimization

2005 ◽  
Vol 15 (2) ◽  
pp. 301-306 ◽  
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Unconstrained Optimization ◽  
Optimization Problems ◽  
Directional Derivative ◽  
Second Order ◽  
General Algorithm ◽  
Unconstrained Optimization Problems ◽  
Convergence Proof

In this paper an algorithm for LC1 unconstrained optimization problems, which uses the second order Dini upper directional derivative is considered. The purpose of the paper is to establish general algorithm hypotheses under which convergence occurs to optimal points. A convergence proof is given, as well as an estimate of the rate of convergence.

scholarly journals A trust region algorithm for lc1 unconstrained optimization

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 285-290
Author(s):  
Nada Djuranovic-Milicic
Keyword(s):  
Rate Of Convergence ◽  
Unconstrained Optimization ◽  
Directional Derivative ◽  
Trust Region ◽  
Second Order ◽  
Trust Region Algorithm ◽  
Lipschitzian Functions ◽  
Convergence Proof ◽  
Locally Lipschitzian Functions

In this paper a trust region algorithm for minimization of locally Lipschitzian functions, which uses the second order Dini upper directional derivative is considered. A convergence proof is given, as well as an estimate of the rate of convergence. .

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