|
|
پژوهش های ریاضی، جلد ۶، شماره ۲، صفحات ۲۱۵-۲۲۴
|
|
|
| عنوان فارسی |
یک الگوریتم تصویری پیش‌رو – پس‌رو برای تقریب ریشۀ مجموع دو عملگر |
|
| چکیده فارسی مقاله |
یک الگوریتم تصویری پیش‌رو-پس‌رو برای یافتن ریشۀ مجموع دو عملگر غیرخطی در فضای هیلبرت را در نظر می‌گیریم. دنبالۀ تولید شده به‌وسیلۀ الگوریتم به‌صورت قوی همگرا به ریشۀ مجموع دو عملگر ![""]("file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image001.png") -به‌طور قوی یکنوای معکوس و یکنوای ماکسیمال است. نتیجه به‌دست آمده را برای حل مسئلۀ نامساوی تغییراتی، مسئلۀ نقطه ثابت و مسئلۀ تعادل به‌کار می‌بریم.
|
|
| کلیدواژه‌های فارسی مقاله |
عملگر یکنوای ماکسیمال، عملگر حلال، الگوریتم تصویری پیش‌رو – پس‌رو. |
|
| عنوان انگلیسی |
A Forward-Backward Projection Algorithm for Approximating of the Zero of the Sum of Two Operators |
|
| چکیده انگلیسی مقاله |
Introduction
One of the most important classes of mappings is the class of monotone mappings due to its various applications. For solving many important problems, it is required to solve monotone inclusion problems, for instance, evolution equations, convex optimization problems, complementarity problems and variational inequalities problems.
The first algorithm for approximating the zero points of the monotone operator introduced by Martinet. In the past decades, many authors prepared various algorithms and investigated the existence and convergence of zero points for maximal monotone mappings in Hilbert spaces.
A generalization of finding zero points of nonlinear operator is to find zero points of the sum of an ![""]("file:///C:Users1AppDataLocalTempmsohtmlclip11clip_image002.gif") -inverse strongly monotone operator and a maximal monotone operator. Passty introduced an iterative methods so called forward-backward method for finding zero points of the sum of two operators. There are various applications of the problem of finding zero points of the sum of two operators.
Recently, some authors introduced and studied some algorithms for finding zero points of the sum of a -inverse strongly monotone operator and a maximal monotone operator under different conditions.
In this paper, motivated and inspired in above, a shrinking projection algorithm is introduced for finding zero points of the sum of an inverse strongly monotone operator and a maximal monotone operator. We prove the strong convergence theorem under mild restrictions imposed on the control sequences.
Material and methods
In this scheme, first we gather some definitions and lemmas of geometry of Banach spaces and monotone operators, which will be needed in the remaining sections. In the next section, a shrinking projection algorithm is proposed and a strong convergence theorem is established for finding a zero point of the sum of an inverse strongly monotone operator and a maximal monotone operator.
Results and discussion
The generated sequence by the presented algorithm converges strongly to a zero point of the sum of an -inverse strongly monotone operator and a maximal monotone operator in Hilbert spaces.
Conclusion
In this paper, we present an iterative algorithm for approximating a zero point of the sum of an -inverse strongly monotone operator and a maximal monotone operator in Hilbert spaces. - Under some mild conditions, we show the convergence theorem of the mentioned algorithm. Subsequently, some corollaries and applications of those main result is provided.
- This observation may lead to the future works that are to analyze and discuss the rate of convergence of these suggested algorithms.
- We obtain some applications of main theorem for solving variational inequality problems and finding fixed points of strict pseudocontractions../files/site1/files/62/7Abstract.pdf
|
|
| کلیدواژه‌های انگلیسی مقاله |
Maximal monotone operator, Resolvent operator, Forward-backward projection algorithm. |
|
| نویسندگان مقاله |
وحید داداشی | Vahid Dadashi
دانشگاه آزاد اسلامی، واحد ساری، گروه ریاضی
|
|
| نشانی اینترنتی |
http://mmr.khu.ac.ir/browse.php?a_code=A-10-403-1&slc_lang=fa&sid=1 |
| فایل مقاله |
فایلی برای مقاله ذخیره نشده است |
| کد مقاله (doi) |
|
| زبان مقاله منتشر شده |
fa |
| موضوعات مقاله منتشر شده |
جبر |
| نوع مقاله منتشر شده |
علمی پژوهشی بنیادی |
|
|
|
برگشت به:
صفحه اول پایگاه |
نسخه مرتبط |
نشریه مرتبط |
فهرست نشریات
|
