Set-valued mappings and enlargements of monotone operators
Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, i...
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Springer
2017
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oai:112.137.131.14:VNU_123-298182020-06-17T08:51:05Z Set-valued mappings and enlargements of monotone operators Iusem, Alfredo N. Burachik, Regina S. Mathematics Statistics ; Monotone operators. 515.724 Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms. 2017-04-17T07:20:22Z 2017-04-17T07:20:22Z 2008 Book 978-0-387-69755-0 http://repository.vnu.edu.vn/handle/VNU_123/29818 en 305 p. application/pdf Springer |
| institution |
Đại học Quốc Gia Hà Nội |
| collection |
DSpace |
| language |
English |
| topic |
Mathematics Statistics ; Monotone operators. 515.724 |
| spellingShingle |
Mathematics Statistics ; Monotone operators. 515.724 Iusem, Alfredo N. Burachik, Regina S. Set-valued mappings and enlargements of monotone operators |
| description |
Set-valued analysis is an essential tool for the mathematical formulation of many real-life situations, e.g., equilibrium theory in mathematical economics. This work offers the first comprehensive treatment in book form of the fairly new subdiscipline of enlargements of maximal monotone operators, including several important new results in the field. In the last decades, with the development of nonsmooth optimization, effective algorithms have been developed to solve these kinds of problems, such as nonsmooth variational inequalities. Several of these methods, such as bundle methods for variational problems, are fully developed and analyzed in this book. The first chapters provide a self-contained review of the basic notions and fundamental results in set-valued analysis, including set convergence and continuity of set-valued mappings together with many important results in infinite-dimensional convex analysis, leading to the classical fixed point results due to Ekeland, Caristi and Kakutani. Next, an in-depth introduction to monotone operators is developed, emphasizing results related to maximality of subdifferentials and of sums of monotone operators. Building on this foundational material, the second part of the monograph contains new results (all of them established during the last decade) on the concept of enlargements of monotone operators, with applications to variational inequalities, bundle-type methods, augmented Lagrangian methods, and proximal point algorithms. |
| format |
Book |
| author |
Iusem, Alfredo N. Burachik, Regina S. |
| author_facet |
Iusem, Alfredo N. Burachik, Regina S. |
| author_sort |
Iusem, Alfredo N. |
| title |
Set-valued mappings and enlargements of monotone operators |
| title_short |
Set-valued mappings and enlargements of monotone operators |
| title_full |
Set-valued mappings and enlargements of monotone operators |
| title_fullStr |
Set-valued mappings and enlargements of monotone operators |
| title_full_unstemmed |
Set-valued mappings and enlargements of monotone operators |
| title_sort |
set-valued mappings and enlargements of monotone operators |
| publisher |
Springer |
| publishDate |
2017 |
| url |
http://repository.vnu.edu.vn/handle/VNU_123/29818 |
| work_keys_str_mv |
AT iusemalfredon setvaluedmappingsandenlargementsofmonotoneoperators AT burachikreginas setvaluedmappingsandenlargementsofmonotoneoperators |
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1787736219017281536 |