LEADER 04235nam 2200541 450 001 996495167603316 005 20230421131542.0 010 $a3-031-13078-2 035 $a(MiAaPQ)EBC7127691 035 $a(Au-PeEL)EBL7127691 035 $a(CKB)25219360300041 035 $a(PPN)265856507 035 $a(EXLCZ)9925219360300041 100 $a20230316d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMaximum-entropy sampling $ealgorithms and application /$fMarcia Fampa and Jon Lee 210 1$aCham, Switzerland :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (206 pages) 225 1 $aSpringer series in operations research 311 08$aPrint version: Fampa, Marcia Maximum-Entropy Sampling Cham : Springer International Publishing AG,c2022 9783031130779 320 $aIncludes bibliographical references (pages 183-191) and index. 327 $aIntro -- Preface -- Overview -- Notation -- Contents -- The problem and basic properties -- Differential entropy -- The MESP and the CMESP -- Hardness -- A solvable case -- The complementary problem -- Scaling -- Masks -- Submodularity -- Branch-and-bound -- The branch-and-bound algorithmic framework for MESP -- Global upper bound for early termination -- Good lower bounds -- Greedy -- Swapping -- Approximation algorithm -- The branch-and-bound algorithmic framework for CMESP -- Upper bounds -- Spectral bounds -- Unconstrained -- Constrained -- Integer linear optimization -- An ILP-based diagonal bound for CMESP -- An ILP-based partition bound for MESP -- linx bound -- Convexity of linx -- Duality for linx -- Fixing variables in linx -- Computing linx and Dlinx solutions -- Scaling for linx -- The complementary problem of linx-gamma -- Factorization bound -- The Lagrangian dual of Fact -- Duality for DFact -- Fixing variables in DDFact -- Computing DDFact and DFact solutions -- Properties of the factorization bound -- NLP bound -- Convexity of NLP -- Scaling for NLP -- Good parameters for NLPgamma -- Strategies to select parameters for NLPgamma -- Duality and the logarithmic-barrier problem for gNLP -- Fixing variables in gNLP -- The logarithmic-barrier algorithm for gNLP -- NLP-gamma in the branch-and-bound algorithm -- BQP bound -- Convexity of BQP -- Duality for BQP -- Fixing variables in BQP -- A good feasible solution of DBQP from BQP -- Scaling for BQP -- Mixing bounds -- The mixing framework -- Optimizing the mixing parameters -- Duality for mixing -- Fixing variables in mix -- A good feasible solution of Dmix from mix -- Mixing the BQPgamma bound with the complementary BQPgamma bound -- Duality for smBQP -- Fixing variables in smBQP -- A good feasible solution of DsmBQP from smBQP -- Comparison of bounds -- Environmental monitoring. 327 $aThe setting -- MESP within statistics and optimal experimental design -- MESP and environmental statistics -- From raw data to covariance matrices -- An example -- Opportunities -- Developing algorithmic advances for MESP/CMESP -- Variable fixing and branch-and-bound: state of the art -- Optimizing gamma for NLPgamma -- Solvable cases of MESP and mask optimization -- OA for CMESP -- MESP/CMESP variations and cousins -- Applications -- Basic formulae and inequalities -- Preliminary miscellany -- Square matrices -- Symmetric matrices -- Positive definite and semidefinite matrices -- References -- Index. 410 0$aSpringer series in operations research. 606 $aMathematical optimization 606 $aMaximum entropy method 606 $aMathematical optimization$xMethodology 606 $aOptimització matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical optimization. 615 0$aMaximum entropy method. 615 0$aMathematical optimization$xMethodology. 615 7$aOptimització matemàtica 676 $a519.3 700 $aFampa$b Marcia$01264085 702 $aLee$b Jon 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996495167603316 996 $aMaximum-entropy sampling$93065688 997 $aUNISA