A polynomial case of the cardinality-constrained quadratic optimization problem

Jianjun Gao and Duan Li ()

Journal of Global Optimization, 2013, vol. 56, issue 4, 1455 pages

Abstract: We propose in this paper a fixed parameter polynomial algorithm for the cardinality-constrained quadratic optimization problem, which is NP-hard in general. More specifically, we prove that, given a problem of size n (the number of decision variables) and s (the cardinality), if the n−k largest eigenvalues of the coefficient matrix of the problem are identical for some 0 > k ≤ n, we can construct a solution algorithm with computational complexity of $${\mathcal{O}\left(n^{2k}\right)}$$ . Note that this computational complexity is independent of the cardinality s and is achieved by decomposing the primary problem into several convex subproblems, where the total number of the subproblems is determined by the cell enumeration algorithm for hyperplane arrangement in $${\mathbb{R}^k}$$ space. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Cardinality-constrained quadratic optimization; Cell enumeration; Nonconvex optimization; Fixed parameter polynomial algorithm (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9853-z

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