科研之友
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摘要
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 being the number of decision variables and being the possible integer values of each decision variable, if the largest eigenvalues of the quadratic coefficient matrix in the objective function are identical for some , we can construct a solution algorithm with a computational complexity of . 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 space, which can be efficiently identified by cell enumeration algorithm.
