یک اصلاح کاهشی مقیاس‌بندی شده از روش گرادیان مزدوج هستنس-اشتیفل با نگاه کاربردی در حسگری فشرده

الموضوعات :

علی ابراهیم نژاد ¹ , زهره امینی فرد ² , سامان بابایی کفاکی ³

1 - (1) گروه ریاضی، واحد قائم¬شهر، دانشگاه آزاد اسلامی، قائم¬شهر، ایران
2 - (2) دانشکده ریاضی، آمار و علوم کامپیوتر، دانشگاه سمنان، سمنان، ایران
3 - (2) دانشکده ریاضی، آمار و علوم کامپیوتر، دانشگاه سمنان، سمنان، ایران

تاريخ الإرسال : 19 السبت , جمادى الثانية, 1443 تاريخ التأكيد : 30 الأحد , رمضان, 1443 تاريخ الإصدار : 06 الخميس , رجب, 1445

الکلمات المفتاحية: compressed sensing, unconstrained optimization, sufficient descent property, Global convergence, conjugate gradient method,

ملخص المقالة :

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.

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