{"product_id":"9783540560975","title":"Lecture Notes in Economics and Mathematical Systems","description":"\u003ch1\u003eLecture Notes in Economics and Mathematical Systems\u003c\/h1\u003e \u003ch2\u003eFrauendorfer, Karl\u003c\/h2\u003e \u003cp\u003eStochastic Programming offers models and methods for\ndecision problems wheresome of the data are uncertain.\nThese models have features and structural   properties which\nare preferably exploited by SP methods within the          solution\nprocess. This work contributes to the methodology for\ntwo-stagemodels. In these models the objective function is\ngiven as an integral,     whose integrand depends on a random\nvector, on its probability measure and  on a decision.\nThe main results of this work have been derived with         the\nintention to ease these difficulties: After investigating\nduality   relations for convex optimization problems with\nsupply\/demand and prices    being treated as parameters, a\nstability criterion is stated and            proves\nsubdifferentiability of the value function. This criterion\nis    employed for proving the existence of bilinear functions,\nwhich             minorize\/majorize the integrand. Additionally, these\nminorants\/majorants    support the integrand on generalized\nbarycenters of simplicial faces of     specially shaped\npolytopes and amount to an approach which is               denoted\nbarycentric approximation scheme.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 1992-12-17\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783540560975\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-642-95696-6\u003c\/p\u003e \u003cp\u003eDimensions: 242cm x170cm\u003c\/p\u003e \u003cp\u003ePages: 228\u003c\/p\u003e ","brand":"Springer Berlin Heidelberg","offers":[{"title":"Default Title","offer_id":44398516830348,"sku":"9783540560975","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783540560975.jpg?v=1774028649","url":"https:\/\/lateknightbooks.com\/products\/9783540560975","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}