یک الگوریتم نقطه مبدایی ترکیبی برای عملگر حلال در فضای باناخ
محورهای موضوعی : آمار
1 - گروه ریاضی، دانشکده علوم پایه، واحد ساری، دانشگاه آزاد اسلامی، ساری، ایران
2 - گروه ریاضی، دانشکده علوم پایه، واحد ساری، دانشگاه آزاد اسلامی، ساری، ایران
کلید واژه: maximal monotone operator, Equilibrium problem, proximal point algorithm, the resolvent operator in Banach space,
چکیده مقاله :
مسئلههای تعادل کاربردهای فراوانی در نظریه بهینه سازی و آنالیز محدب دارند و به همین دلیل است که روش‌های متفاوتی برای حل مسئلههای تعادل درفضاهای مختلف از جمله فضاهای هیلبرت و فضاهای باناخ ارائه شده است. هدف این مقاله، ارائه روشی برای به دست آوردن جواب مسئله تعادل در فضاهای باناخ می‌باشد. در واقع، یک الگوریتم نقطه مبدایی ترکیبی با استفاده از حلال یک عملگر یکنوای ماکسیمال در فضای باناخ را در نظر میگیریم. تحت شرایطی مناسب، همگرایی قوی دنباله تولید شده توسط الگوریتم به ریشه عملگر یکنوای ماکسیمال را ثابت میکنیم. به عنوان کاربردی از نتیجه اصلی و با استفاده از قضایای ثابت شده، برای هر دوتابع یکنوا میتوانیم یک عملگر یکنوای ماکسیمال ارائه کنیم به طوریکه، ریشه عملگر یکنوای ماکسیمال همان جواب مسئله تعادل باشد. نتایج این مقاله، تعدادی از نتایج حاصل شده در مقالات مختلف را تعمیم داده یا بهبود میبخشد.
Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm using the resolvent of a maximal monotone operator in Banach space. Under appropriate conditions, we prove the strong convergence of the generated sequence by the algorithm to the zero of the maximal monotone operator. As an application of the main result, and using proved theorems, we can provide a maximal monotone operator for any monotone bifunction so that the zero of the maximal monotone operator is the solution to the equilibrium problem. The results of this paper generalize or improve the obtained results in the various papers.
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