Conic Approximations and Collinear Scalings for Optimizers

1980 ◽  
Vol 17 (2) ◽  
pp. 268-281 ◽  
Author(s):  
William C. Davidon
Keyword(s):  
Collinear Scalings ◽  
Conic Approximations

A CONIC AFFINE SCALING DOGLEG METHOD FOR NONLINEAR OPTIMIZATION WITH BOUND CONSTRAINTS

2013 ◽  
Vol 30 (03) ◽  
pp. 1340011 ◽  
Author(s):  
LIJUAN ZHAO ◽  
WENYU SUN
Keyword(s):  
Quadratic Model ◽  
Affine Scaling ◽  
Bound Constraints ◽  
Siam Journal ◽  
Standard Testing ◽  
Conic Model ◽  
Mild Conditions ◽  
Numerical Tests ◽  
Collinear Scalings ◽  
Conic Approximations

The conic model proposed by Davidon (1980) [Davidon, WC (1980). Conic approximations and collinear scalings for optimizers. SIAM Journal on Numerical Analysis, 17, 268–281.] is an extension of quadratic model incorporating more information than quadratic model. In this paper, we propose a conic affine scaling dogleg method for bound constrained optimization. Under some mild conditions, the sequence generated by our algorithm converges to a stationary point. Numerical tests on a series of standard testing problems confirm the efficiency of the method.

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