Robust Optimization / / Aharon Ben-Tal, Arkadi Nemirovski, Laurent El Ghaoui.
Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of r...
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Ben-Tal, Aharon, author. aut http://id.loc.gov/vocabulary/relators/aut Robust Optimization / Aharon Ben-Tal, Arkadi Nemirovski, Laurent El Ghaoui. Course Book Princeton, NJ : Princeton University Press, [2009] ©2009 1 online resource (576 p.) : 36 line illus. 41 tables. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Series in Applied Mathematics ; 28 Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Robust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject. 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) Linear programming. Robust optimization. MATHEMATICS / Linear & Nonlinear Programming. bisacsh 0O. Accuracy and precision. Additive model. Almost surely. Approximation algorithm. Approximation. Best, worst and average case. Bifurcation theory. Big O notation. Candidate solution. Central limit theorem. Chaos theory. Coefficient. Computational complexity theory. Constrained optimization. Convex hull. Convex optimization. Convex set. Cumulative distribution function. Curse of dimensionality. Decision problem. Decision rule. Degeneracy (mathematics). Diagram (category theory). Duality (optimization). Dynamic programming. Exponential function. Feasible region. Floor and ceiling functions. For All Practical Purposes. Free product. Ideal solution. Identity matrix. Inequality (mathematics). Infimum and supremum. Integer programming. Law of large numbers. Likelihood-ratio test. Linear dynamical system. Linear inequality. Linear map. Linear matrix inequality. Linear regression. Loss function. Margin classifier. Markov chain. Markov decision process. Mathematical optimization. Max-plus algebra. Maxima and minima. Multivariate normal distribution. NP-hardness. Norm (mathematics). Normal distribution. Optimal control. Optimization problem. Orientability. P versus NP problem. Pairwise. Parameter. Parametric family. Probability distribution. Probability. Proportionality (mathematics). Quantity. Random variable. Relative interior. Robust control. Robust decision-making. Semi-infinite. Sensitivity analysis. Simple set. Singular value. Skew-symmetric matrix. Slack variable. Special case. Spherical model. Spline (mathematics). State variable. Stochastic calculus. Stochastic control. Stochastic optimization. Stochastic programming. Stochastic. Strong duality. Support vector machine. Theorem. Time complexity. Uncertainty. Uniform distribution (discrete). Unimodality. Upper and lower bounds. Variable (mathematics). Virtual displacement. Weak duality. Wiener filter. With high probability. Without loss of generality. El Ghaoui, Laurent, author. aut http://id.loc.gov/vocabulary/relators/aut Nemirovski, Arkadi, 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 9780691143682 https://doi.org/10.1515/9781400831050 https://www.degruyter.com/isbn/9781400831050 Cover https://www.degruyter.com/document/cover/isbn/9781400831050/original |
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English |
format |
eBook |
author |
Ben-Tal, Aharon, Ben-Tal, Aharon, El Ghaoui, Laurent, Nemirovski, Arkadi, |
spellingShingle |
Ben-Tal, Aharon, Ben-Tal, Aharon, El Ghaoui, Laurent, Nemirovski, Arkadi, Robust Optimization / Princeton Series in Applied Mathematics ; Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index |
author_facet |
Ben-Tal, Aharon, Ben-Tal, Aharon, El Ghaoui, Laurent, Nemirovski, Arkadi, El Ghaoui, Laurent, El Ghaoui, Laurent, Nemirovski, Arkadi, Nemirovski, Arkadi, |
author_variant |
a b t abt a b t abt g l e gl gle a n an |
author_role |
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author2 |
El Ghaoui, Laurent, El Ghaoui, Laurent, Nemirovski, Arkadi, Nemirovski, Arkadi, |
author2_variant |
g l e gl gle a n an |
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VerfasserIn VerfasserIn VerfasserIn VerfasserIn |
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Ben-Tal, Aharon, |
title |
Robust Optimization / |
title_full |
Robust Optimization / Aharon Ben-Tal, Arkadi Nemirovski, Laurent El Ghaoui. |
title_fullStr |
Robust Optimization / Aharon Ben-Tal, Arkadi Nemirovski, Laurent El Ghaoui. |
title_full_unstemmed |
Robust Optimization / Aharon Ben-Tal, Arkadi Nemirovski, Laurent El Ghaoui. |
title_auth |
Robust Optimization / |
title_alt |
Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index |
title_new |
Robust Optimization / |
title_sort |
robust optimization / |
series |
Princeton Series in Applied Mathematics ; |
series2 |
Princeton Series in Applied Mathematics ; |
publisher |
Princeton University Press, |
publishDate |
2009 |
physical |
1 online resource (576 p.) : 36 line illus. 41 tables. Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Part I. Robust Linear Optimization -- Chapter One. Uncertain Linear Optimization Problems and their Robust Counterparts -- Chapter Two. Robust Counterpart Approximations of Scalar Chance Constraints -- Chapter Three. Globalized Robust Counterparts of Uncertain LO Problems -- Chapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints -- Part II. Robust Conic Optimization -- Chapter Five. Uncertain Conic Optimization: The Concepts -- Chapter Six. Uncertain Conic Quadratic Problems with Tractable RCs -- Chapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems -- Chapter Eight. Uncertain Semidefinite Problems with Tractable RCs -- Chapter Nine. Approximating RCs of Uncertain Semidefinite Problems -- Chapter Ten. Approximating Chance Constrained CQIs and LMIs -- Chapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems -- Chapter Twelve. Robust Classi¯cation and Estimation -- Part III. Robust Multi-Stage Optimization -- Chapter Thirteen. Robust Markov Decision Processes -- Chapter Fourteen. Robust Adjustable Multistage Optimization -- Part IV. Selected Applications -- Chapter Fifteen. Selected Applications -- Appendix A: Notation and Prerequisites -- Appendix B: Some Auxiliary Proofs -- Appendix C: Solutions to Selected Exercises -- Bibliography -- Index |
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Q - Science |
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QA - Mathematics |
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QA402 |
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QA 3402.5 B445 42009EB |
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https://doi.org/10.1515/9781400831050 https://www.degruyter.com/isbn/9781400831050 https://www.degruyter.com/document/cover/isbn/9781400831050/original |
illustrated |
Illustrated |
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500 - Science |
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510 - Mathematics |
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519 - Probabilities & applied mathematics |
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519.6 |
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" 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">Orientability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">P versus NP problem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Pairwise.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parameter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Parametric family.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability distribution.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Probability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Proportionality (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Quantity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Random variable.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Relative interior.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Robust control.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Robust decision-making.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Robust optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Semi-infinite.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Sensitivity analysis.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Simple set.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Singular value.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Skew-symmetric matrix.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Slack variable.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Special case.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spherical model.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Spline (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">State variable.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic calculus.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic control.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic optimization.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic programming.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Stochastic.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Strong duality.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Support vector machine.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Theorem.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Time complexity.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Uncertainty.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Uniform distribution (discrete).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Unimodality.</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 (mathematics).</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Virtual displacement.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Weak duality.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Wiener filter.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">With high probability.</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Without loss of generality.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">El Ghaoui, Laurent, </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">Nemirovski, Arkadi, </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 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