{"product_id":"multilevel-optimization-algorithms-and-applications-9781461379898","title":"Multilevel Optimization: Algorithms and Applications","description":"\u003cp\u003e • Author(s): A. Migdalas\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Applied\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\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\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45283828662423,"sku":"9781461379898","price":14553.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781461379898.webp?v=1769306025","url":"https:\/\/atlanticbooks.com\/products\/multilevel-optimization-algorithms-and-applications-9781461379898","provider":"Atlantic Books","version":"1.0","type":"link"}