Geodesic
Solution of One Problem of Choice of Products by Means of Branch and Bound Method
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 38-50

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In article the mixed-integer linear programming problem (with binary variables) is considered. This problem is NP-complete as generalizes knapsack problem. The new way of calculation of bounds in branch and bound method is offered. The way is based on transition to a dual problem in continuous variables and on known minimax theorems. The numerical example illustrates features of such approach. 
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     author = {R. M. Larin and E. V. Hmel},
     title = {Solution of {One} {Problem} of {Choice} of {Products} by {Means} of {Branch} and {Bound} {Method}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {38--50},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a3/}
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R. M. Larin; E. V. Hmel. Solution of One Problem of Choice of Products by Means of Branch and Bound Method. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 8 (2008) no. 1, pp. 38-50. http://geodesic.mathdoc.fr/item/VNGU_2008_8_1_a3/