# American Institute of Mathematical Sciences

July  2014, 10(3): 945-963. doi: 10.3934/jimo.2014.10.945

## Quadratic optimization over one first-order cone

 1 Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China 2 Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, United States, United States

Received  February 2013 Revised  June 2013 Published  November 2013

This paper studies the first-order cone constrained homogeneous quadratic programming problem. For efficient computation, the problem is reformulated as a linear conic programming problem. A union of second-order cones are designed to cover the first-order cone such that a sequence of linear conic programming problems can be constructed to approximate the conic reformulation. Since the cone of nonnegative quadratic forms over a union of second-order cones has a linear matrix inequalities representation, each linear conic programming problem in the sequence is polynomial-time solvable by applying semidefinite programming techniques. The convergence of the sequence is guaranteed when the union of second-order cones gets close enough to the first-order cone. In order to further improve the efficiency, an adaptive scheme is adopted. Numerical experiments are provided to illustrate the efficiency of the proposed approach.
Citation: Xiaoling Guo, Zhibin Deng, Shu-Cherng Fang, Wenxun Xing. Quadratic optimization over one first-order cone. Journal of Industrial & Management Optimization, 2014, 10 (3) : 945-963. doi: 10.3934/jimo.2014.10.945
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##### References:
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