یک اصلاح کاهشی مقیاس‌بندی شده از روش گرادیان مزدوج هستنس-اشتیفل با نگاه کاربردی در حسگری فشرده
محورهای موضوعی : تحقیق در عملیات
علی ابراهیم نژاد
1
((1) گروه ریاضی، واحد قائم¬شهر، دانشگاه آزاد اسلامی، قائم¬شهر، ایران)
زهره امینی فرد
2
((2) دانشکده ریاضی، آمار و علوم کامپیوتر، دانشگاه سمنان، سمنان، ایران)
سامان بابایی کفاکی
3
((2) دانشکده ریاضی، آمار و علوم کامپیوتر، دانشگاه سمنان، سمنان، ایران)
کلید واژه: compressed sensing, unconstrained optimization, sufficient descent property, Global convergence, conjugate gradient method,
چکیده مقاله :
به منظور بهبود روش گرادیان مزدوج کلاسیک هستنس-اشتیفل، شنگوی و همکاران یک روش گرادیان مزدوج موثر را پیشنهاد کردند که با استفاده از جستجوی خطی ولف قوی (با محدود کردن پارامترهای جستجوی خطی) در خاصیت کافی کاهشی ‎صدق می کند. با الهام از توسیع مقیاس بندی شده ی روش هستنس-اشتیفل که اخیرا توسط دانگ و همکاران مطرح شده است، یک اصلاح مقیاس بندی شده از روش گرادیان مزدوج شنگوی و همکاران پیشنهاد می شود که قادر است شرط کافی کاهشی را مستقل از تکنیک جستجوی خطی و بدون فرض تحدب تابع هدف برقرار سازد. همچنین، همگرایی سراسری روش مطرح شده بر اساس فرضیات استاندارد مورد بحث قرار می‌گیرد. به علاوه، یک تقریب هموار برای مساله بهینه‌سازی حسگری فشرده ارائه می شود. عملکرد عددی بر مجموعه‌ای از مسائل کلاسیک از کتابخانه CUTEr و نیز در حل مساله حسگری فشرده مورد ارزیابی قرار می گیرد. نتایج مقایسات برتری رویکرد پیشنهادی را به تصویر می کشند.
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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