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020 _a9783662025581
_9978-3-662-02558-1
024 7 _a10.1007/978-3-662-02558-1
_2doi
050 4 _aHD30.23
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_2bicssc
072 7 _aBUS049000
_2bisacsh
072 7 _aKJT
_2thema
072 7 _aKJMD
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082 0 4 _a658.40301
100 1 _aMarti, Kurt.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aDescent Directions and Efficient Solutions in Discretely Distributed Stochastic Programs
_h[electronic resource] /
_cby Kurt Marti.
250 _a1st ed. 1988.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1988.
300 _aXIV, 183 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Economics and Mathematical Systems,
_x0075-8442 ;
_v299
505 0 _aContents: Stochastic programs with a discrete distribution -- Stochastic dominance (SD) and the construction of feasible descent directions -- Convex programs for solving (3.1)-(3.4a),(3.5) -- Stationary points (efficient solutions) of (SOP) -- Optimal solutions of (Px,D),(Px,D) -- Optimal solutions (y*,T*) of (Px,D) having Tij>0 for all i S,j R -- Existence of solutions of the SD-conditions (3.1.)-(3.5), (12.1)-(12.5), resp; Representation of stationary points -- Construction of solutions (y,T) of (12.1)-12.4) by means of formula (44) -- Construction of solutions (y,B) of (46) by using representation (60) of (A( ),b( )),- References -- Index.
520 _aIn engineering and economics a certain vector of inputs or decisions must often be chosen, subject to some constraints, such that the expected costs arising from the deviation between the output of a stochastic linear system and a desired stochastic target vector are minimal. In many cases the loss function u is convex and the occuring random variables have, at least approximately, a joint discrete distribution. Concrete problems of this type are stochastic linear programs with recourse, portfolio optimization problems, error minimization and optimal design problems. In solving stochastic optimization problems of this type by standard optimization software, the main difficulty is that the objective function F and its derivatives are defined by multiple integrals. Hence, one wants to omit, as much as possible, the time-consuming computation of derivatives of F. Using the special structure of the problem, the mathematical foundations and several concrete methods for the computation of feasible descent directions, in a certain part of the feasible domain, are presented first, without any derivatives of the objective function F. It can also be used to support other methods for solving discretely distributed stochastic programs, especially large scale linear programming and stochastic approximation methods.
650 0 _aOperations research.
650 0 _aDecision making.
650 0 _aEconomic theory.
650 0 _aSystem theory.
650 0 _aCalculus of variations.
650 0 _aApplied mathematics.
650 0 _aEngineering mathematics.
650 1 4 _aOperations Research/Decision Theory.
_0https://scigraph.springernature.com/ontologies/product-market-codes/521000
650 2 4 _aEconomic Theory/Quantitative Economics/Mathematical Methods.
_0https://scigraph.springernature.com/ontologies/product-market-codes/W29000
650 2 4 _aSystems Theory, Control.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M13070
650 2 4 _aCalculus of Variations and Optimal Control; Optimization.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M26016
650 2 4 _aMathematical and Computational Engineering.
_0https://scigraph.springernature.com/ontologies/product-market-codes/T11006
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783540187783
776 0 8 _iPrinted edition:
_z9783662025598
830 0 _aLecture Notes in Economics and Mathematical Systems,
_x0075-8442 ;
_v299
856 4 0 _uhttps://s443-doi-org.br.lsproxy.net/10.1007/978-3-662-02558-1
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