e-ISSN 2231-8542
ISSN 1511-3701

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Preconditioned Subspace Quasi-Newton Method for Large Scale Optimization

Hong Seng Sim, Wah June Leong, Malik Abu Hassan and Fudziah Ismail

Pertanika Journal of Tropical Agricultural Science, Volume 22, Issue 1, January 2014

Keywords: Preconditioned, subspace method, limited memory quasi-Newton methods, large scale, unconstrained optimization

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Subspace quasi-Newton (SQN) method has been widely used in large scale unconstrained optimization problem. Its popularity is due to the fact that the method can construct subproblems in low dimensions so that storage requirement as well as the computation cost can be minimized. However, the main drawback of the SQN method is that it can be very slow on certain types of non-linear problem such as ill-conditioned problems. Hence, we proposed a preconditioned SQN method, which is generally more effective than the SQN method. In order to achieve this, we proposed that a diagonal updating matrix that was derived based on the weak secant relation be used instead of the identity matrix to approximate the initial inverse Hessian. Our numerical results show that the proposed preconditioned SQN method performs better than the SQN method which is without preconditioning.

ISSN 1511-3701

e-ISSN 2231-8542

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