Self-Regularity : : A New Paradigm for Primal-Dual Interior-Point Algorithms / / Jiming Peng, Tamás Terlaky, Cornelis Roos.
Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap b...
Saved in:
Superior document: | Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
---|---|
VerfasserIn: | |
Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2009] ©2003 |
Year of Publication: | 2009 |
Edition: | Course Book |
Language: | English |
Series: | Princeton Series in Applied Mathematics ;
22 |
Online Access: | |
Physical Description: | 1 online resource (208 p.) |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
id |
9781400825134 |
---|---|
ctrlnum |
(DE-B1597)446375 (OCoLC)979757457 |
collection |
bib_alma |
record_format |
marc |
spelling |
Peng, Jiming, author. aut http://id.loc.gov/vocabulary/relators/aut Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / Jiming Peng, Tamás Terlaky, Cornelis Roos. Course Book Princeton, NJ : Princeton University Press, [2009] ©2003 1 online resource (208 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Series in Applied Mathematics ; 22 Frontmatter -- Contents -- Preface -- Acknowledgments -- Notation -- List of Abbreviations -- Chapter 1. Introduction and Preliminaries -- Chapter 2. Self-Regular Functions and Their Properties -- Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- Chapter 8. Conclusions -- References -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) MATHEMATICS / Applied. bisacsh Accuracy and precision. Algorithm. Analysis of algorithms. Analytic function. Associative property. Barrier function. Binary number. Block matrix. Combination. Combinatorial optimization. Combinatorics. Complexity. Conic optimization. Continuous optimization. Control theory. Convex optimization. Delft University of Technology. Derivative. Differentiable function. Directional derivative. Division by zero. Dual space. Duality (mathematics). Duality gap. Eigenvalues and eigenvectors. Embedding. Equation. Estimation. Existential quantification. Explanation. Feasible region. Filter design. Function (mathematics). Implementation. Instance (computer science). Invertible matrix. Iteration. Jacobian matrix and determinant. Jordan algebra. Karmarkar's algorithm. Karush-Kuhn-Tucker conditions. Line search. Linear complementarity problem. Linear function. Linear programming. Lipschitz continuity. Local convergence. Loss function. Mathematical optimization. Mathematician. Mathematics. Matrix function. McMaster University. Monograph. Multiplication operator. Newton's method. Nonlinear programming. Nonlinear system. Notation. Operations research. Optimal control. Optimization problem. Parameter (computer programming). Parameter. Pattern recognition. Polyhedron. Polynomial. Positive semidefinite. Positive-definite matrix. Quadratic function. Requirement. Result. Scientific notation. Second derivative. Self-concordant function. Sensitivity analysis. Sign (mathematics). Signal processing. Simplex algorithm. Simultaneous equations. Singular value. Smoothness. Solution set. Solver. Special case. Subset. Suggestion. Technical report. Theorem. Theory. Time complexity. Two-dimensional space. Upper and lower bounds. Variable (computer science). Variable (mathematics). Variational inequality. Variational principle. Without loss of generality. Worst-case complexity. Yurii Nesterov. Roos, Cornelis, author. aut http://id.loc.gov/vocabulary/relators/aut Terlaky, Tamás, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package 9783110515831 ZDB-23-PAM Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691091938 https://doi.org/10.1515/9781400825134?locatt=mode:legacy https://www.degruyter.com/isbn/9781400825134 Cover https://www.degruyter.com/document/cover/isbn/9781400825134/original |
language |
English |
format |
eBook |
author |
Peng, Jiming, Peng, Jiming, Roos, Cornelis, Terlaky, Tamás, |
spellingShingle |
Peng, Jiming, Peng, Jiming, Roos, Cornelis, Terlaky, Tamás, Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / Princeton Series in Applied Mathematics ; Frontmatter -- Contents -- Preface -- Acknowledgments -- Notation -- List of Abbreviations -- Chapter 1. Introduction and Preliminaries -- Chapter 2. Self-Regular Functions and Their Properties -- Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- Chapter 8. Conclusions -- References -- Index |
author_facet |
Peng, Jiming, Peng, Jiming, Roos, Cornelis, Terlaky, Tamás, Roos, Cornelis, Roos, Cornelis, Terlaky, Tamás, Terlaky, Tamás, |
author_variant |
j p jp j p jp c r cr t t tt |
author_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author2 |
Roos, Cornelis, Roos, Cornelis, Terlaky, Tamás, Terlaky, Tamás, |
author2_variant |
c r cr t t tt |
author2_role |
VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
author_sort |
Peng, Jiming, |
title |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / |
title_sub |
A New Paradigm for Primal-Dual Interior-Point Algorithms / |
title_full |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / Jiming Peng, Tamás Terlaky, Cornelis Roos. |
title_fullStr |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / Jiming Peng, Tamás Terlaky, Cornelis Roos. |
title_full_unstemmed |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / Jiming Peng, Tamás Terlaky, Cornelis Roos. |
title_auth |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / |
title_alt |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Notation -- List of Abbreviations -- Chapter 1. Introduction and Preliminaries -- Chapter 2. Self-Regular Functions and Their Properties -- Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- Chapter 8. Conclusions -- References -- Index |
title_new |
Self-Regularity : |
title_sort |
self-regularity : a new paradigm for primal-dual interior-point algorithms / |
series |
Princeton Series in Applied Mathematics ; |
series2 |
Princeton Series in Applied Mathematics ; |
publisher |
Princeton University Press, |
publishDate |
2009 |
physical |
1 online resource (208 p.) Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Acknowledgments -- Notation -- List of Abbreviations -- Chapter 1. Introduction and Preliminaries -- Chapter 2. Self-Regular Functions and Their Properties -- Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- Chapter 8. Conclusions -- References -- Index |
isbn |
9781400825134 9783110515831 9783110442502 9780691091938 |
url |
https://doi.org/10.1515/9781400825134?locatt=mode:legacy https://www.degruyter.com/isbn/9781400825134 https://www.degruyter.com/document/cover/isbn/9781400825134/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
519 - Probabilities & applied mathematics |
dewey-full |
519.6 |
dewey-sort |
3519.6 |
dewey-raw |
519.6 |
dewey-search |
519.6 |
doi_str_mv |
10.1515/9781400825134?locatt=mode:legacy |
oclc_num |
979757457 |
work_keys_str_mv |
AT pengjiming selfregularityanewparadigmforprimaldualinteriorpointalgorithms AT rooscornelis selfregularityanewparadigmforprimaldualinteriorpointalgorithms AT terlakytamas selfregularityanewparadigmforprimaldualinteriorpointalgorithms |
status_str |
n |
ids_txt_mv |
(DE-B1597)446375 (OCoLC)979757457 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
is_hierarchy_title |
Self-Regularity : A New Paradigm for Primal-Dual Interior-Point Algorithms / |
container_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
author2_original_writing_str_mv |
noLinkedField noLinkedField noLinkedField noLinkedField |
_version_ |
1806143522013708288 |
fullrecord |
<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>08740nam a22019215i 4500</leader><controlfield tag="001">9781400825134</controlfield><controlfield tag="003">DE-B1597</controlfield><controlfield tag="005">20220131112047.0</controlfield><controlfield tag="006">m|||||o||d||||||||</controlfield><controlfield tag="007">cr || ||||||||</controlfield><controlfield tag="008">220131t20092003nju fo d z eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400825134</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9781400825134</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-B1597)446375</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)979757457</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-B1597</subfield><subfield code="b">eng</subfield><subfield code="c">DE-B1597</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">nju</subfield><subfield code="c">US-NJ</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT003000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">519.6</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Peng, Jiming, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Self-Regularity :</subfield><subfield code="b">A New Paradigm for Primal-Dual Interior-Point Algorithms /</subfield><subfield code="c">Jiming Peng, Tamás Terlaky, Cornelis Roos.</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">Course Book</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ : </subfield><subfield code="b">Princeton University Press, </subfield><subfield code="c">[2009]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">©2003</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (208 p.)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">text file</subfield><subfield code="b">PDF</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Princeton Series in Applied Mathematics ;</subfield><subfield code="v">22</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Frontmatter -- </subfield><subfield code="t">Contents -- </subfield><subfield code="t">Preface -- </subfield><subfield code="t">Acknowledgments -- </subfield><subfield code="t">Notation -- </subfield><subfield code="t">List of Abbreviations -- </subfield><subfield code="t">Chapter 1. Introduction and Preliminaries -- </subfield><subfield code="t">Chapter 2. Self-Regular Functions and Their Properties -- </subfield><subfield code="t">Chapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- </subfield><subfield code="t">Chapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- </subfield><subfield code="t">Chapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- </subfield><subfield code="t">Chapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- </subfield><subfield code="t">Chapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- </subfield><subfield code="t">Chapter 8. Conclusions -- </subfield><subfield code="t">References -- </subfield><subfield code="t">Index</subfield></datafield><datafield tag="506" ind1="0" ind2=" "><subfield code="a">restricted access</subfield><subfield code="u">http://purl.org/coar/access_right/c_16ec</subfield><subfield code="f">online access with authorization</subfield><subfield code="2">star</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Research on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work.</subfield></datafield><datafield tag="530" ind1=" " ind2=" "><subfield code="a">Issued also in print.</subfield></datafield><datafield tag="538" ind1=" " ind2=" "><subfield code="a">Mode of access: Internet via World Wide Web.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Applied.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Accuracy and precision.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Algorithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Analysis of algorithms.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Analytic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Associative property.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Barrier function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Binary number.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Block matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Combination.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Combinatorial optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Combinatorics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Complexity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Conic optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Continuous optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Control theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Convex optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Delft University of Technology.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Differentiable function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Directional derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Division by zero.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Dual space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Duality (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Duality gap.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Eigenvalues and eigenvectors.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Embedding.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Equation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Estimation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Existential quantification.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Explanation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Feasible region.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Filter design.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Function (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Implementation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Instance (computer science).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Invertible matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Iteration.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Jacobian matrix and determinant.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Jordan algebra.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Karmarkar's algorithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Karush-Kuhn-Tucker conditions.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Line search.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Linear complementarity problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Linear function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Linear programming.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Lipschitz continuity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Local convergence.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Loss function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematical optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematician.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Mathematics.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Matrix function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">McMaster University.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Monograph.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Multiplication operator.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Newton's method.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nonlinear programming.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Nonlinear system.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Operations research.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Optimal control.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Optimization problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parameter (computer programming).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parameter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pattern recognition.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polyhedron.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Polynomial.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Positive semidefinite.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Positive-definite matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quadratic function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Requirement.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Result.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Scientific notation.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Second derivative.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Self-concordant function.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sensitivity analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sign (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Signal processing.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simplex algorithm.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simultaneous equations.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Singular value.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Smoothness.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Solution set.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Solver.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Subset.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Suggestion.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Technical report.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theory.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Time complexity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Two-dimensional space.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Upper and lower bounds.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (computer science).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variable (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variational inequality.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Variational principle.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Without loss of generality.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Worst-case complexity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Yurii Nesterov.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Roos, Cornelis, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Terlaky, Tamás, </subfield><subfield code="e">author.</subfield><subfield code="4">aut</subfield><subfield code="4">http://id.loc.gov/vocabulary/relators/aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton Series in Applied Mathematics eBook-Package</subfield><subfield code="z">9783110515831</subfield><subfield code="o">ZDB-23-PAM</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Title is part of eBook package:</subfield><subfield code="d">De Gruyter</subfield><subfield code="t">Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="z">9783110442502</subfield></datafield><datafield tag="776" ind1="0" ind2=" "><subfield code="c">print</subfield><subfield code="z">9780691091938</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://doi.org/10.1515/9781400825134?locatt=mode:legacy</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://www.degruyter.com/isbn/9781400825134</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="3">Cover</subfield><subfield code="u">https://www.degruyter.com/document/cover/isbn/9781400825134/original</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">978-3-11-044250-2 Princeton University Press eBook-Package Backlist 2000-2013</subfield><subfield code="c">2000</subfield><subfield code="d">2013</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_BACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_CL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBACKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ECL_MTPY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_EEBKALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_ESTMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_PPALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">EBA_STMALL</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV-deGruyter-alles</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA12STME</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA13ENGE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA18STMEE</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">PDA5EBK</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-23-PAM</subfield></datafield></record></collection> |