{"product_id":"9780792346937","title":"Multilevel Optimization: Algorithms and Applications","description":"Researchers 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).","brand":"Athanasios Migdalas, Panos M. Pardalos, Peter Varbrand","offers":[{"title":"Default Title","offer_id":45857784332606,"sku":"9780792346937","price":6018.31,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9780792346937_fc003f98-c311-4c83-beda-784547c81247.jpg?v=1707326881","url":"https:\/\/exclusivebooks.co.za\/products\/9780792346937","provider":"Exclusive Books Online","version":"1.0","type":"link"}