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http://dx.doi.org/10.15207/JKCS.2016.7.5.213

An Algorithm for the Singly Linearly Constrained Concave Minimization Problem with Upper Convergent Bounded Variables  

Oh, Se-Ho (Dept. of Industrial Engineering, Cheongju University)
Publication Information
Journal of the Korea Convergence Society / v.7, no.5, 2016 , pp. 213-219 More about this Journal
Abstract
This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.
Keywords
Branch-and-bound; Concave minimization; Convex envelope; Partition; Simplex;
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Times Cited By KSCI : 7  (Citation Analysis)
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