{ "item_title" : "Multilevel Optimization", "item_author" : [" A. Migdalas", "Panos M. Pardalos", "Peter Värbrand "], "item_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).", "item_img_path" : "https://covers3.booksamillion.com/covers/bam/1/46/137/989/146137989X_b.jpg", "price_data" : { "retail_price" : "219.99", "online_price" : "219.99", "our_price" : "219.99", "club_price" : "219.99", "savings_pct" : "0", "savings_amt" : "0.00", "club_savings_pct" : "0", "club_savings_amt" : "0.00", "discount_pct" : "10", "store_price" : "" } }

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