LEADER 08418nam 2201885Ia 450 001 9910778219003321 005 20230106005421.0 010 $a1-282-25928-8 010 $a9786612259289 010 $a1-4008-3105-9 024 7 $a10.1515/9781400831050 035 $a(CKB)1000000000788528 035 $a(EBL)457706 035 $a(OCoLC)439040007 035 $a(SSID)ssj0000239025 035 $a(PQKBManifestationID)11220773 035 $a(PQKBTitleCode)TC0000239025 035 $a(PQKBWorkID)10235249 035 $a(PQKB)11591388 035 $a(MiAaPQ)EBC457706 035 $a(DE-B1597)447001 035 $a(OCoLC)979757917 035 $a(DE-B1597)9781400831050 035 $a(Au-PeEL)EBL457706 035 $a(CaPaEBR)ebr10326354 035 $a(CaONFJC)MIL225928 035 $a(PPN)170242854 035 $a(EXLCZ)991000000000788528 100 $a20090414d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRobust optimization$b[electronic resource] /$fAharon Ben-Tal, Laurent El Ghaoui, Arkadi Nemirovski 205 $aCourse Book 210 $aPrinceton, NJ $cPrinceton University Press$dc2009 215 $a1 online resource (565 p.) 225 0 $aPrinceton Series in Applied Mathematics ;$v28 300 $aDescription based upon print version of record. 311 $a0-691-14368-4 327 $tFrontmatter --$tContents --$tPreface --$tPart I. Robust Linear Optimization --$tChapter One. Uncertain Linear Optimization Problems and their Robust Counterparts --$tChapter Two. Robust Counterpart Approximations of Scalar Chance Constraints --$tChapter Three. Globalized Robust Counterparts of Uncertain LO Problems --$tChapter Four. More on Safe Tractable Approximations of Scalar Chance Constraints --$tPart II. Robust Conic Optimization --$tChapter Five. Uncertain Conic Optimization: The Concepts --$tChapter Six. Uncertain Conic Quadratic Problems with Tractable RCs --$tChapter Seven. Approximating RCs of Uncertain Conic Quadratic Problems --$tChapter Eight. Uncertain Semidefinite Problems with Tractable RCs --$tChapter Nine. Approximating RCs of Uncertain Semidefinite Problems --$tChapter Ten. Approximating Chance Constrained CQIs and LMIs --$tChapter Eleven. Globalized Robust Counterparts of Uncertain Conic Problems --$tChapter Twelve. Robust Classi¯cation and Estimation --$tPart III. Robust Multi-Stage Optimization --$tChapter Thirteen. Robust Markov Decision Processes --$tChapter Fourteen. Robust Adjustable Multistage Optimization --$tPart IV. Selected Applications --$tChapter Fifteen. Selected Applications --$tAppendix A: Notation and Prerequisites --$tAppendix B: Some Auxiliary Proofs --$tAppendix C: Solutions to Selected Exercises --$tBibliography --$tIndex 330 $aRobust optimization is still a relatively new approach to optimization problems affected by uncertainty, but it has already proved so useful in real applications that it is difficult to tackle such problems today without considering this powerful methodology. Written by the principal developers of robust optimization, and describing the main achievements of a decade of research, this is the first book to provide a comprehensive and up-to-date account of the subject. Robust optimization is designed to meet some major challenges associated with uncertainty-affected optimization problems: to operate under lack of full information on the nature of uncertainty; to model the problem in a form that can be solved efficiently; and to provide guarantees about the performance of the solution. The book starts with a relatively simple treatment of uncertain linear programming, proceeding with a deep analysis of the interconnections between the construction of appropriate uncertainty sets and the classical chance constraints (probabilistic) approach. It then develops the robust optimization theory for uncertain conic quadratic and semidefinite optimization problems and dynamic (multistage) problems. The theory is supported by numerous examples and computational illustrations. An essential book for anyone working on optimization and decision making under uncertainty, Robust Optimization also makes an ideal graduate textbook on the subject. 410 0$aPrinceton Series in Applied Mathematics 606 $aRobust optimization 606 $aLinear programming 610 $a0O. 610 $aAccuracy and precision. 610 $aAdditive model. 610 $aAlmost surely. 610 $aApproximation algorithm. 610 $aApproximation. 610 $aBest, worst and average case. 610 $aBifurcation theory. 610 $aBig O notation. 610 $aCandidate solution. 610 $aCentral limit theorem. 610 $aChaos theory. 610 $aCoefficient. 610 $aComputational complexity theory. 610 $aConstrained optimization. 610 $aConvex hull. 610 $aConvex optimization. 610 $aConvex set. 610 $aCumulative distribution function. 610 $aCurse of dimensionality. 610 $aDecision problem. 610 $aDecision rule. 610 $aDegeneracy (mathematics). 610 $aDiagram (category theory). 610 $aDuality (optimization). 610 $aDynamic programming. 610 $aExponential function. 610 $aFeasible region. 610 $aFloor and ceiling functions. 610 $aFor All Practical Purposes. 610 $aFree product. 610 $aIdeal solution. 610 $aIdentity matrix. 610 $aInequality (mathematics). 610 $aInfimum and supremum. 610 $aInteger programming. 610 $aLaw of large numbers. 610 $aLikelihood-ratio test. 610 $aLinear dynamical system. 610 $aLinear inequality. 610 $aLinear map. 610 $aLinear matrix inequality. 610 $aLinear programming. 610 $aLinear regression. 610 $aLoss function. 610 $aMargin classifier. 610 $aMarkov chain. 610 $aMarkov decision process. 610 $aMathematical optimization. 610 $aMax-plus algebra. 610 $aMaxima and minima. 610 $aMultivariate normal distribution. 610 $aNP-hardness. 610 $aNorm (mathematics). 610 $aNormal distribution. 610 $aOptimal control. 610 $aOptimization problem. 610 $aOrientability. 610 $aP versus NP problem. 610 $aPairwise. 610 $aParameter. 610 $aParametric family. 610 $aProbability distribution. 610 $aProbability. 610 $aProportionality (mathematics). 610 $aQuantity. 610 $aRandom variable. 610 $aRelative interior. 610 $aRobust control. 610 $aRobust decision-making. 610 $aRobust optimization. 610 $aSemi-infinite. 610 $aSensitivity analysis. 610 $aSimple set. 610 $aSingular value. 610 $aSkew-symmetric matrix. 610 $aSlack variable. 610 $aSpecial case. 610 $aSpherical model. 610 $aSpline (mathematics). 610 $aState variable. 610 $aStochastic calculus. 610 $aStochastic control. 610 $aStochastic optimization. 610 $aStochastic programming. 610 $aStochastic. 610 $aStrong duality. 610 $aSupport vector machine. 610 $aTheorem. 610 $aTime complexity. 610 $aUncertainty. 610 $aUniform distribution (discrete). 610 $aUnimodality. 610 $aUpper and lower bounds. 610 $aVariable (mathematics). 610 $aVirtual displacement. 610 $aWeak duality. 610 $aWiener filter. 610 $aWith high probability. 610 $aWithout loss of generality. 615 0$aRobust optimization. 615 0$aLinear programming. 676 $a519.6 686 $aSK 870$2rvk 700 $aBen-Tal$b A$01567721 701 $aEl Ghaoui$b Laurent$028454 701 $aNemirovskii?$b Arkadii? Semenovich$0725351 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910778219003321 996 $aRobust optimization$93839318 997 $aUNINA