LEADER 08558nam 22020415 450 001 9910813827803321 005 20210114161929.0 010 $a1-282-08760-6 010 $a9786612087608 010 $a1-4008-2513-X 024 7 $a10.1515/9781400825134 035 $a(CKB)1000000000756257 035 $a(EBL)445420 035 $a(OCoLC)355680042 035 $a(SSID)ssj0000243846 035 $a(PQKBManifestationID)11923120 035 $a(PQKBTitleCode)TC0000243846 035 $a(PQKBWorkID)10168565 035 $a(PQKB)10716548 035 $a(DE-B1597)446375 035 $a(OCoLC)979757457 035 $a(DE-B1597)9781400825134 035 $z(PPN)199244596 035 $a(MiAaPQ)EBC445420 035 $a(PPN)187949883 035 $a(EXLCZ)991000000000756257 100 $a20190708d2009 fg 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSelf-Regularity $eA New Paradigm for Primal-Dual Interior-Point Algorithms /$fJiming Peng, Cornelis Roos, Tamás Terlaky 205 $aCourse Book 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2009] 210 4$d©2003 215 $a1 online resource (201 p.) 225 0 $aPrinceton Series in Applied Mathematics ;$v22 300 $aDescription based upon print version of record. 311 $a0-691-09193-5 327 $t Frontmatter -- $tContents -- $tPreface -- $tAcknowledgments -- $tNotation -- $tList of Abbreviations -- $tChapter 1. Introduction and Preliminaries -- $tChapter 2. Self-Regular Functions and Their Properties -- $tChapter 3. Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities -- $tChapter 4. Interior-Point Methods for Complementarity Problems Based on Self- Regular Proximities -- $tChapter 5. Primal-Dual Interior-Point Methods for Semidefinite Optimization Based on Self-Regular Proximities -- $tChapter 6. Primal-Dual Interior-Point Methods for Second-Order Conic Optimization Based on Self-Regular Proximities -- $tChapter 7. Initialization: Embedding Models for Linear Optimization, Complementarity Problems, Semidefinite Optimization and Second-Order Conic Optimization -- $tChapter 8. Conclusions -- $tReferences -- $tIndex 330 $aResearch on interior-point methods (IPMs) has dominated the field of mathematical programming for the last two decades. Two contrasting approaches in the analysis and implementation of IPMs are the so-called small-update and large-update methods, although, until now, there has been a notorious gap between the theory and practical performance of these two strategies. This book comes close to bridging that gap, presenting a new framework for the theory of primal-dual IPMs based on the notion of the self-regularity of a function. The authors deal with linear optimization, nonlinear complementarity problems, semidefinite optimization, and second-order conic optimization problems. The framework also covers large classes of linear complementarity problems and convex optimization. The algorithm considered can be interpreted as a path-following method or a potential reduction method. Starting from a primal-dual strictly feasible point, the algorithm chooses a search direction defined by some Newton-type system derived from the self-regular proximity. The iterate is then updated, with the iterates staying in a certain neighborhood of the central path until an approximate solution to the problem is found. By extensively exploring some intriguing properties of self-regular functions, the authors establish that the complexity of large-update IPMs can come arbitrarily close to the best known iteration bounds of IPMs. Researchers and postgraduate students in all areas of linear and nonlinear optimization will find this book an important and invaluable aid to their work. 410 0$aPrinceton Series in Applied Mathematics 606 $aInterior-point methods 606 $aMathematical optimization 606 $aMathematical optimization 606 $aProgramming (Mathematics) 606 $aMathematical optimization 606 $aInterior-point methods 606 $aProgramming (Mathematics) 606 $aCivil & Environmental Engineering$2HILCC 606 $aEngineering & Applied Sciences$2HILCC 606 $aOperations Research$2HILCC 610 $aAccuracy and precision. 610 $aAlgorithm. 610 $aAnalysis of algorithms. 610 $aAnalytic function. 610 $aAssociative property. 610 $aBarrier function. 610 $aBinary number. 610 $aBlock matrix. 610 $aCombination. 610 $aCombinatorial optimization. 610 $aCombinatorics. 610 $aComplexity. 610 $aConic optimization. 610 $aContinuous optimization. 610 $aControl theory. 610 $aConvex optimization. 610 $aDelft University of Technology. 610 $aDerivative. 610 $aDifferentiable function. 610 $aDirectional derivative. 610 $aDivision by zero. 610 $aDual space. 610 $aDuality (mathematics). 610 $aDuality gap. 610 $aEigenvalues and eigenvectors. 610 $aEmbedding. 610 $aEquation. 610 $aEstimation. 610 $aExistential quantification. 610 $aExplanation. 610 $aFeasible region. 610 $aFilter design. 610 $aFunction (mathematics). 610 $aImplementation. 610 $aInstance (computer science). 610 $aInvertible matrix. 610 $aIteration. 610 $aJacobian matrix and determinant. 610 $aJordan algebra. 610 $aKarmarkar's algorithm. 610 $aKarush?Kuhn?Tucker conditions. 610 $aLine search. 610 $aLinear complementarity problem. 610 $aLinear function. 610 $aLinear programming. 610 $aLipschitz continuity. 610 $aLocal convergence. 610 $aLoss function. 610 $aMathematical optimization. 610 $aMathematician. 610 $aMathematics. 610 $aMatrix function. 610 $aMcMaster University. 610 $aMonograph. 610 $aMultiplication operator. 610 $aNewton's method. 610 $aNonlinear programming. 610 $aNonlinear system. 610 $aNotation. 610 $aOperations research. 610 $aOptimal control. 610 $aOptimization problem. 610 $aParameter (computer programming). 610 $aParameter. 610 $aPattern recognition. 610 $aPolyhedron. 610 $aPolynomial. 610 $aPositive semidefinite. 610 $aPositive-definite matrix. 610 $aQuadratic function. 610 $aRequirement. 610 $aResult. 610 $aScientific notation. 610 $aSecond derivative. 610 $aSelf-concordant function. 610 $aSensitivity analysis. 610 $aSign (mathematics). 610 $aSignal processing. 610 $aSimplex algorithm. 610 $aSimultaneous equations. 610 $aSingular value. 610 $aSmoothness. 610 $aSolution set. 610 $aSolver. 610 $aSpecial case. 610 $aSubset. 610 $aSuggestion. 610 $aTechnical report. 610 $aTheorem. 610 $aTheory. 610 $aTime complexity. 610 $aTwo-dimensional space. 610 $aUpper and lower bounds. 610 $aVariable (computer science). 610 $aVariable (mathematics). 610 $aVariational inequality. 610 $aVariational principle. 610 $aWithout loss of generality. 610 $aWorst-case complexity. 610 $aYurii Nesterov. 615 4$aInterior-point methods. 615 4$aMathematical optimization. 615 4$aMathematical optimization. 615 4$aProgramming (Mathematics). 615 0$aMathematical optimization 615 0$aInterior-point methods 615 0$aProgramming (Mathematics) 615 7$aCivil & Environmental Engineering 615 7$aEngineering & Applied Sciences 615 7$aOperations Research 676 $a519.6 700 $aPeng$b Jiming, $0726750 702 $aRoos$b Cornelis, 702 $aTerlaky$b Tamás, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910813827803321 996 $aSelf-Regularity$93924874 997 $aUNINA