| 000 -LEADER |
|---|
| fixed length control field |
05884nam a2200889 i 4500 |
| 001 - CONTROL NUMBER |
|---|
| control field |
6813202 |
| 003 - CONTROL NUMBER IDENTIFIER |
|---|
| control field |
IEEE |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
|---|
| control field |
20200413152912.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS |
|---|
| fixed length control field |
m eo d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
|---|
| fixed length control field |
cr cn |||m|||a |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
|---|
| fixed length control field |
140113s2014 caua foab 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| International Standard Book Number |
9781627052382 |
| Qualifying information |
ebook |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
|---|
| Canceled/invalid ISBN |
9781627052375 |
| Qualifying information |
paperback |
| 024 7# - OTHER STANDARD IDENTIFIER |
|---|
| Standard number or code |
10.2200/S00554ED1V01Y201312MAS014 |
| Source of number or code |
doi |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(CaBNVSL)swl00403028 |
| 035 ## - SYSTEM CONTROL NUMBER |
|---|
| System control number |
(OCoLC)868155830 |
| 040 ## - CATALOGING SOURCE |
|---|
| Original cataloging agency |
CaBNVSL |
| Language of cataloging |
eng |
| Description conventions |
rda |
| Transcribing agency |
CaBNVSL |
| Modifying agency |
CaBNVSL |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
|---|
| Classification number |
QA639.5 |
| Item number |
.M674 2014 |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
|---|
| Classification number |
516.08 |
| Edition number |
23 |
| 090 ## - LOCALLY ASSIGNED LC-TYPE CALL NUMBER (OCLC); LOCAL CALL NUMBER (RLIN) |
|---|
| Classification number (OCLC) (R) ; Classification number, CALL (RLIN) (NR) |
|
| Local cutter number (OCLC) ; Book number/undivided call number, CALL (RLIN) |
MoCl |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
|---|
| Personal name |
Mordukhovich, B. Sh. |
| Fuller form of name |
(Boris Sholimovich), |
| Relator term |
author. |
| 245 13 - TITLE STATEMENT |
|---|
| Title |
An easy path to convex analysis and applications / |
| Statement of responsibility, etc. |
Boris S. Mordukhovich, Nguyen Mau Nam. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
San Rafael, California (1537 Fourth Street, San Rafael, CA 94901 USA) : |
| Name of producer, publisher, distributor, manufacturer |
Morgan & Claypool, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2014. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
1 PDF (xvi, 202 pages) : |
| Other physical details |
illustrations. |
| 336 ## - CONTENT TYPE |
|---|
| Content type term |
text |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
|---|
| Media type term |
electronic |
| Source |
isbdmedia |
| 338 ## - CARRIER TYPE |
|---|
| Carrier type term |
online resource |
| Source |
rdacarrier |
| 490 1# - SERIES STATEMENT |
|---|
| Series statement |
Synthesis lectures on mathematics and statistics, |
| International Standard Serial Number |
1938-1751 ; |
| Volume/sequential designation |
# 14 |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
Mode of access: World Wide Web. |
| 538 ## - SYSTEM DETAILS NOTE |
|---|
| System details note |
System requirements: Adobe Acrobat Reader. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Part of: Synthesis digital library of engineering and computer science. |
| 500 ## - GENERAL NOTE |
|---|
| General note |
Series from website. |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE |
|---|
| Bibliography, etc. note |
Includes bibliographical references (pages 195-197) and index. |
| 505 0# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
1. Convex sets and functions -- 1.1 Preliminaries -- 1.2 Convex sets -- 1.3 Convex functions -- 1.4 Relative interiors of convex sets -- 1.5 The distance function -- 1.6 Exercises for chapter 1 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
2. Subdifferential calculus -- 2.1 Convex separation -- 2.2 Normals to convex sets -- 2.3 Lipschitz continuity of convex functions -- 2.4 Subgradients of convex functions -- 2.5 Basic calculus rules -- 2.6 Subgradients of optimal value functions -- 2.7 Subgradients of support functions -- 2.8 Fenchel conjugates -- 2.9 Directional derivatives -- 2.10 Subgradients of supremum functions -- 2.11 Exercises for chapter 2 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
3. Remarkable consequences of convexity -- 3.1 Characterizations of differentiability -- 3.2 Carathéodory theorem and Farkas Lemma -- 3.3 Radon theorem and Helly theorem -- 3.4 Tangents to convex sets -- 3.5 Mean value theorems -- 3.6 Horizon cones -- 3.7 Minimal time functions and Minkowski gauge -- 3.8 Subgradients of minimal time functions -- 3.9 Nash equilibrium -- 3.10 Exercises for chapter 3 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
4. Applications to optimization and location problems -- 4.1 Lower semicontinuity and existence of minimizers -- 4.2 Optimality conditions -- 4.3 Subgradient methods in convex optimization -- 4.4 The Fermat-Torricelli problem -- 4.5 A generalized Fermat-Torricelli problem -- 4.6 A generalized Sylvester problem -- 4.7 Exercises for chapter 4 -- |
| 505 8# - FORMATTED CONTENTS NOTE |
|---|
| Formatted contents note |
Solutions and hints for exercises -- Bibliography -- Authors' biographies -- Index. |
| 506 1# - RESTRICTIONS ON ACCESS NOTE |
|---|
| Terms governing access |
Abstract freely available; full-text restricted to subscribers or individual document purchasers. |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Compendex |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
INSPEC |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google scholar |
| 510 0# - CITATION/REFERENCES NOTE |
|---|
| Name of source |
Google book search |
| 520 3# - SUMMARY, ETC. |
|---|
| Summary, etc. |
Convex optimization has an increasing impact on many areas of mathematics, applied sciences, and practical applications. It is now being taught at many universities and being used by researchers of different fields. As convex analysis is the mathematical foundation for convex optimization, having deep knowledge of convex analysis helps students and researchers apply its tools more effectively. The main goal of this book is to provide an easy access to the most fundamental parts of convex analysis and its applications to optimization. Modern techniques of variational analysis are employed to clarify and simplify some basic proofs in convex analysis and build the theory of generalized differentiation for convex functions and sets in finite dimensions. We also present new applications of convex analysis to location problems in connection with many interesting geometric problems such as the Fermat-Torricelli problem, the Heron problem, the Sylvester problem, and their generalizations. Of course, we do not expect to touch every aspect of convex analysis, but the book consists of sufficient material for a first course on this subject. It can also serve as supplemental reading material for a course on convex optimization and applications. |
| 530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE |
|---|
| Additional physical form available note |
Also available in print. |
| 588 ## - SOURCE OF DESCRIPTION NOTE |
|---|
| Source of description note |
Title from PDF title page (viewed on January 13, 2014). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Convex geometry. |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Affine set |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Carathéodory theorem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
convex function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
convex set |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
directional derivative |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
distance function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Fenchel conjugate |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Fermat-Torricelli problem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
generalized differentiation |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Helly theorem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
minimal time function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Nash equilibrium |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
normal cone |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Radon theorem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
optimal value function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
optimization |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
smallest enclosing ball problem |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
set-valued mapping |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
subdifferential |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
subgradient |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
subgradient algorithm |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
support function |
| 653 ## - INDEX TERM--UNCONTROLLED |
|---|
| Uncontrolled term |
Weiszfeld algorithm |
| 700 1# - ADDED ENTRY--PERSONAL NAME |
|---|
| Personal name |
Nam, Nguyen Mau., |
| Relator term |
author. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Print version: |
| International Standard Book Number |
9781627052375 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis digital library of engineering and computer science. |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Synthesis lectures on mathematics and statistics ; |
| Volume/sequential designation |
# 14. |
| International Standard Serial Number |
1938-1751 |
| 856 42 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to resource |
| Uniform Resource Identifier |
http://ieeexplore.ieee.org/servlet/opac?bknumber=6813202 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Materials specified |
Abstract with links to full text |
| Uniform Resource Identifier |
http://dx.doi.org/10.2200/S00554ED1V01Y201312MAS014 |
