{"product_id":"linear-and-integer-programming-vs-linear-integration-and-counting-a-duality-viewpoint-von-jean-bernard-lasserre","title":"Linear and Integer Programming vs Linear Integration and Counting","description":"\u003cp\u003eInteger programming (IP) is a fascinating topic. Indeed, while linear programming (LP), its c- tinuous analogue, is well understood and extremely ef?cient LP software packages exist, solving an integer program can remain a formidable challenge, even for some small size problems. For instance, the following small (5-variable) IP problem (called the unbounded knapsack problem) min{213x?1928x?11111x?2345x +9123x} 1 2 3 4 5 s.t. 12223x +12224x +36674x +61119x +85569x = 89643482, 1 2 3 4 5 x ,x ,x ,x ,x?N, 1 2 3 4 5 taken from a list of dif?cult knapsack problems in Aardal and Lenstra [2], is not solved even by hours of computing, using for instance the last version of the ef?cient software package CPLEX. However,thisisnotabookonintegerprogramming,asverygoodonesonthistopicalreadyexist. For standard references on the theory and practice of integer programming, the interested reader is referred to, e.g., Nemhauser and Wolsey [113], Schrijver [121], Wolsey [136], and the more recent Bertsimas and Weismantel [21]. On the other hand, this book could provide a complement to the above books as it develops a rather unusual viewpoint.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9780387094137\"\u003e\u003ch3\u003eA Duality Viewpoint\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9781441918536\"\u003e\u003ch3\u003eA Duality Viewpoint\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Hardcover - 9780387094137","offer_id":39641945636957,"sku":"9780387094137","price":106.99,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9781441918536","offer_id":39415017308253,"sku":"9781441918536","price":106.99,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/ba6c1b4b-85ec-4c99-9154-b112b3a771dd.jpg?v=1772168807","url":"https:\/\/shop.autorenwelt.de\/en\/products\/linear-and-integer-programming-vs-linear-integration-and-counting-a-duality-viewpoint-von-jean-bernard-lasserre","provider":"Autorenwelt Shop","version":"1.0","type":"link"}