A scaled descent modification of the Hestense-Stiefel conjugate gradient method with application to compressed sensing

Subject Areas : تحقیق در عملیات

Ali Ebrahimnejad ¹ (Department of Mathematics,Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran,)
Zohre Aminifard ² (Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran)
Saman Babaie-Kafaki ³ (Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran)

Received: 2022-01-22 Accepted : 2022-05-01 Published : 2024-01-18

Keywords: بهینه‌سازی نامقید, روش گرادیان مزدوج, خاصیت کافی کاهشی, همگرایی سراسری, حسگری فشرده,

Abstract :

To improve the classic Hestense-Stiefel conjugate gradient method, Shengwei et al. proposed an efficient conjugate gradient method which possesses the sufficient descent property when the line search fulfills the strong Wolfe conditions (by restricting the line search parameters). Inspired by the scaled extension of the Hestense-Stiefel method which is recently presented by Dong et al., a scaled modification of the conjugate gradient method of Shengwei et al. is proposed which satisfies the sufficient descent condition independent of the line search technique as well as the convexity assumption of the objective function. Furthermore, the global convergence of the suggested method is discussed based on standard suppositions. In addition, a smooth approximation for the compressed sensing optimization problem is put forward. Numerical experiments are done on a set of classical problems of the CUTEr library as well as in solving compressed sensing problem. Results of the comparisons illustrate the superiority of the proposed approach.

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