{"product_id":"9781461379898","title":"Multilevel Optimization: Algorithms and Applications","description":"\u003ch3\u003eNonconvex Optimization and Its Applications\u003c\/h3\u003e\u003ch1\u003eMultilevel Optimization: Algorithms and Applications\u003c\/h1\u003e\u003ch3\u003eA. Migdalas | Panos M. Pardalos | Peter Värbrand\u003c\/h3\u003e\u003cdiv\u003e\u003cb\u003eMathematics \/ Optimization\u003c\/b\u003e\u003c\/div\u003e\u003cbr\u003e\u003cdiv\u003eResearchers working with nonlinear programming often claim \"the word is non­ linear\" indicating that real applications require nonlinear modeling. The same is true for other areas such as multi-objective programming (there are always several goals in a real application), stochastic programming (all data is uncer­ tain and therefore stochastic models should be used), and so forth. In this spirit we claim: The word is multilevel. In many decision processes there is a hierarchy of decision makers, and decisions are made at different levels in this hierarchy. One way to handle such hierar­ chies is to focus on one level and include other levels' behaviors as assumptions. Multilevel programming is the research area that focuses on the whole hierar­ chy structure. In terms of modeling, the constraint domain associated with a multilevel programming problem is implicitly determined by a series of opti­ mization problems which must be solved in a predetermined sequence. If only two levels are considered, we have one leader (associated with the upper level) and one follower (associated with the lower level).\u003c\/div\u003e\u003cbr\u003e\u003ctable\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublication Date: \u003c\/td\u003e\n\u003ctd\u003e17 September 2011\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePublisher: \u003c\/td\u003e\n\u003ctd\u003eSpringer US\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eImprint: \u003c\/td\u003e\n\u003ctd\u003eSpringer\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eISBN-13: \u003c\/td\u003e\n\u003ctd\u003e9781461379898\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003eFormat: \u003c\/td\u003e\n\u003ctd\u003ePaperback \/ softback\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003ctr\u003e\n\u003ctd\u003ePage Count: \u003c\/td\u003e\n\u003ctd\u003e386\u003c\/td\u003e\n\u003c\/tr\u003e\n\u003c\/table\u003e","brand":"Springer US","offers":[{"title":"Default Title","offer_id":45578321494156,"sku":"9781461379898","price":197.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9781461379898.jpg?v=1780592442","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9781461379898","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}