NATIONAL BIBLIOGRAPHY NUMBER
Number
۲۳۲۵۹پ
LANGUAGE OF THE ITEM
.Language of Text, Soundtrack etc
per
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
روش های تکراری برای حل مسائل بهینه سازی در فضاهای CAT(o) و انعکاسی
Parallel Title Proper
Iterative Processes For Solving Optimization Problems In CAT(۰) And Reflexive Spaces
First Statement of Responsibility
/سهیلا آذرمی
.PUBLICATION, DISTRIBUTION, ETC
Name of Publisher, Distributor, etc.
: علوم ریاضی
Date of Publication, Distribution, etc.
، ۱۳۹۸
Name of Manufacturer
، راشدی
PHYSICAL DESCRIPTION
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۱۰۲ص
NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
Text of Note
چاپی - الکترونیکی
DISSERTATION (THESIS) NOTE
Dissertation or thesis details and type of degree
دکتری
Discipline of degree
ریاضی محض گرایش آنالیز ریاضی
Date of degree
۱۳۹۸/۰۶/۲۰
Body granting the degree
تبریز
SUMMARY OR ABSTRACT
Text of Note
آنالیزغیرخطی به مطالعه و بررسی خصوصیات نگاشت‌صهای غیرخطی بین فضاهای برداری) یا زیرمجموعه‌صهای آن‌صها (می‌صپردازد .اما ایده‌صی کلی تر این است که نه فقط نگاشت‌صها بلکه فضاها هم می‌صتوانند غیرخطی باشند .بسیاری از مسائل آنالیز تغییراتی، بهینه سازی، نظریه‌صی عملگرهای یکنوا و معادلات دیفرانسیل، می‌صتواند به‌ص صورت مسئله‌صی نقطه ثابتx=Tx فرمول بندی شود .روش‌صهای زیادی برای حل این مسئله در فضاهای هیلبرت و باناخ محدب یکنواخت و هموار یکنواخت وجود دارد .وقتی ما درصدد بسط این روش‌صها به فضای باناخ عمومی برمی‌صآییم با مشکلاتی روبرو می‌صشویم .زیرا بسیاری از مثال‌صهای مفید از انواع نگاشت‌صهای غیر انبساطی درفضاهای هیلبرت دیگر غیرانبساطی سازگار یا حتی غیرانبساطی نیستند .چندین روش برای حل این مسئله وجود دارد که یکی از این روش‌صها استفاده از متر برگمن به جای نرم می‌صباشد .بنابراین در تعاریف انواع نگاشت‌صهای غیر انبساطی از متر برگمن به جای نرم استفاده خواهد شد .این تعاریف بسیار مفید هستند، زیرا عملگرهای مهم زیادی وجود دارند که در این تعاریف صدق می‌صکنند .علاوه بر این زمانی که این تعاریف جدید را با f(x)=۱/۲ x
Text of Note
Nonlinear analysis deals with the study of nonlinear mappings between vector spaces (or subsets of them). But the general idea is that not only maps but also spaces can be nonlinear. Many nonlinear analysis problems such as Convex Analysis, Variational Analysis, Optimization, Monotone Mapping Theory and Differential Equations, can be formulated in the form of the fixed point problem. There are many ways to solve this problem in Hilbert spaces and uniformly convex and uniformly smooth Banach spaces. When we are going to extend these methods to the general reflexive Banach spaces, we encounter some difficulties because many of the useful examples of nonexpansive operators in Hilbert spaces are no longer firmly nonexpansive or even nonexpansive in Banach spaces. There are several ways to overcome these difficulties, one of which is the use of Bregman distance instead of norm. Therefore, the defininitions of types of nonexpansive mappings will be defined with respect to the Bregman distance instead of with respect to the norm. These definitions are useful in the setting of Banach spaces since we have several examples of operators satisfying them. In addition, if we go back to Hilbert spaces and take these new definitions with respect to the function f(x) = 1 2x2, then they coincide with the usual definitions. In this thesis, we introduce new iterative methods for solving various optimization problems in reflexive Banach spaces and CAT (0) spaces. In this direction, in section 2, we propose an iterative algorithm to finding a common fixed point of a finite family of Bregman relativelynonexpansive mappings in reflxive Banach spaces using the generalized Bregman f-projection operator. In section 3, by using products of Moreau-Yosida resolvents, we present an iterative algorithm for finding a common element of the set of minimizers of a finite family of convex functions and a common fixed point of two multivalued hybrid mappings in CAT(0) spaces. Then we propose an iterative method for finding the common element of the minimizers of a finite family of convex functions and the common fixed points of a finite family of quasi-nonexpansive multivalued mappings in Hadamard spaces. In section 4, we introduce a new algorithm for finding a solution of split equality variational inequality problem for inverse strongly monotone operators and a common fixed pointsof a finite family of quasi-nonexpansive mappings which does not require any knowledge of the operator norms.Also some applications and numerical examples of proposed algorithms are presented
PARALLEL TITLE PROPER
Parallel Title
Iterative Processes For Solving Optimization Problems In CAT(۰) And Reflexive Spaces
PERSONAL NAME - PRIMARY RESPONSIBILITY
آذرمی، سهیلا
Azarmi, Soheila
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