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LEADER: 03899mam a22003974a 4500
001 2562302
005 20221012194533.0
008 000104t20002000nyu b 001 0 eng
010 $a 00020825
020 $a0387987053 (hardcover : alk. paper)
035 $a(OCoLC)ocm43311747
035 $9AQQ1402CU
035 $a(NNC)2562302
035 $a2562302
040 $aDLC$cDLC$dC#P$dOrLoB-B
042 $apcc
050 00 $aQA871$b.B694 2000
082 00 $a519.3$221
100 1 $aBonnans, J. F.$q(Joseph Frédéric),$d1957-$0http://id.loc.gov/authorities/names/n92067269
245 10 $aPerturbation analysis of optimization problems /$cJ. Frédéric Bonnans, Alexander Shapiro.
260 $aNew York :$bSpringer,$c[2000], ©2000.
300 $axviii, 601 pages ;$c25 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aSpringer series in operations research
504 $aIncludes bibliographical references (p. [583]-594) and index.
505 00 $g1.$tIntroduction --$g2.$tBackground Material.$g2.1.$tBasic Functional Analysis.$g2.2.$tDirectional Differentiability and Tangent Cones.$g2.3.$tElements of Multifunctions Theory.$g2.4.$tConvex Functions.$g2.5.$tDuality Theory --$g3.$tOptimality Conditions.$g3.1.$tFirst Order Optimality Conditions.$g3.2.$tSecond Order Necessary Conditions.$g3.3.$tSecond Order Sufficient Conditions.$g3.4.$tSpecific Structures.$g3.5.$tNonisolated Minima --$g4.$tStability and Sensitivity Analysis.$g4.1.$tStability of the Optimal Value and Optimal Solutions.$g4.2.$tDirectional Regularity.$g4.3.$tFirst Order Differentiability Analysis of the Optimal Value Function.$g4.4.$tQuantitative Stability of Optimal Solutions and Lagrange Multipliers.$g4.5.$tDirectional Stability of Optimal Solutions.$g4.6.$tQuantitative Stability Analysis by a Reduction Approach.$g4.7.$tSecond Order Analysis in Lipschitz Stable Cases.$g4.8.$tSecond Order Analysis in Holder Stable Cases.$g4.9.$tAdditional Results.
505 80 $g4.10.$tSecond Order Analysis in Functional Spaces --$g5.$tAdditional Material and Applications.$g5.1.$tVariational Inequalities.$g5.2.$tNonlinear Programming.$g5.3.$tSemi-definite Programming.$g5.4.$tSemi-infinite Programming --$g6.$tOptimal Control.$g6.1.$tIntroduction.$g6.2.$tLinear and Semilinear Elliptic Equations.$g6.3.$tOptimal Control of a Semilinear Elliptic Equation.$g6.4.$tThe Obstacle Problem --$g7.$tBibliographical Notes.
520 1 $a"This timely book in the area of optimization focuses on the questions of how solutions of optimization problems behave. Under perturbations and on related, first- and especially second-order optimality conditions. The authors have put together many results that are not easily accessible in the current literature, organizing the material in a consistent manner so that a broad theory emerges.
520 8 $aA considerable body of supporting material, such as elements of convex analysis, duality theory, etc., and applications to nonlinear semi-definite and semi-infinite programming, is presented and may have an independent interest. Many elements are new and not available elsewhere." "In particular, the emphasis is on infinite dimensions as well as finite-dimensional problems.".
520 8 $a"Research professionals, including graduate students at an advanced level in the fields of optimization, nonlinear programming, and optimal control, and also more general users of optimization will find this text useful."--BOOK JACKET.
650 0 $aPerturbation (Mathematics)$0http://id.loc.gov/authorities/subjects/sh85100181
650 0 $aMathematical optimization.$0http://id.loc.gov/authorities/subjects/sh85082127
700 1 $aShapiro, Alexander,$d1949-$0http://id.loc.gov/authorities/names/n00000933
830 0 $aSpringer series in operations research.$0http://id.loc.gov/authorities/names/n94040737
852 00 $boff,eng$hQA871$i.B694 2000