A polynomial case of the cardinality-constrained quadratic optimization problem

  • Authors:

  • Jianjun Gao;Duan Li

  • Affiliations:

  • Department of Automation, The School of Electronic, Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai, People's Republic of China;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2013

Quantified Score

Hi-index 0.00

Visualization

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驴k largest eigenvalues of the coefficient matrix of the problem are identical for some 0 k 驴 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.