A polynomial case of convex integer quadratic programming problems with box integer constraints

Chunli Liu () and Jianjun Gao ()

Journal of Global Optimization, 2015, vol. 62, issue 4, 674 pages

Abstract: In this paper, we study a special class of convex quadratic integer programming problem with box constraints. By using the decomposition approach, we propose a fixed parameter polynomial time algorithm for such a class of problems. Given a problem with size $$n$$ n being the number of decision variables and $$m$$ m being the possible integer values of each decision variable, if the $$n-k$$ n - k largest eigenvalues of the quadratic coefficient matrix in the objective function are identical for some $$k$$ k $$(0>k>n)$$ ( 0 > k > n ) , we can construct a solution algorithm with a computational complexity of $${\mathcal {O}}((mn)^k)$$ O ( ( m n ) k ) . To achieve such complexity, we decompose the original problem into several convex quadratic programming problems, where the total number of the subproblems is bounded by the number of cells generated by a set of hyperplane arrangements in $$\mathbb {R}^k$$ R k space, which can be efficiently identified by cell enumeration algorithm. Copyright Springer Science+Business Media New York 2015

Keywords: Quadratic integer optimization; Polynomial solvable case; Box constrained (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-014-0263-2

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