IJPAM: Volume 52, No. 4 (2009)
Invited Lecture Delivered at
Fourth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)
ON THE STRUCTURE OF VARIABLE METRIC UPDATES
Institute of Control and Computation Engineering
Warsaw University of Technology
15/19, Nowowiejska, Warsaw, 00-665, POLAND
e-mail: [email protected]
Abstract.The key idea of the material presented in the paper is that all commonly used variable metric updates consist of the projection part that nullifies vector parallel to differences of the derivatives of the minimized function and the second one (the same for all known formulae) ensuring verification of the quasi-Newton condition at each step of the method.
In the paper a new class of updates ensuring inheritance of the conjugacy property (when applied to a strictly convex QP problem with exact directional minimization) is introduced. Its properties are analysed and some preliminary computational results on some test problems suggested by Moré [#! more!#] are reported.
Received: August 14, 2007
AMS Subject Classification: 65K05, 90C53
Key Words and Phrases: variable metric methods, affine projections, conjugacy property
Source: International Journal of Pure and Applied Mathematics