Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization

Hong Seng Sim; Wah June Leong; Chuei Yee Chen; Siti Nur Iqmal Ibrahim

doi:10.3934/naco.2018024

Article Contents

2018, Volume 8, Issue 3: 377-387. Doi: 10.3934/naco.2018024

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Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization

1.
Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Sungai Long Campus, Jalan Sungai Long 9, Bandar Sungai Long, 43000 Kajang, Selangor, Malaysia
2.
Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3.
Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

* Corresponding author: Hong Seng Sim
* Corresponding author: Hong Seng Sim

Received: April 30, 2017

Revised: February 28, 2018

Published: June 2018

The first author is supported by Yayasan Sultan Iskandar Johor 2014

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Abstract

In this paper, we aim to propose some spectral gradient methods via variational technique under log-determinant norm. The spectral parameters satisfy the modified weak secant relations that inspired by the multistep approximation for solving large scale unconstrained optimization. An executable code is developed to test the efficiency of the proposed method with spectral gradient method using standard weak secant relation as constraint. Numerical results are presented which suggest a better performance has been achieved.

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Mathematics Subject Classification: Primary: 65K10, 93B40; Secondary: 90C06.

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Figure 1. Performance Profiling for the Modified Multiple Spectral Gradient Methods and Standard Multiple Spectral Gradient Method in terms of Number of Iterations.

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Figure 2. Performance Profiling for the Modified Multiple Spectral Gradient Methods and Standard Multiple Spectral Gradient Method in terms of Number of Function Calls.

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Figure 3. Performance Profiling for the Modified Multiple Spectral Gradient Methods and Standard Multiple Spectral Gradient Method in terms of CPU Time.

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