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January  2016, 12(1): 269-283. doi: 10.3934/jimo.2016.12.269

## Quadratic optimization over a polyhedral cone

 1 School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130 2 Department of Management Science and Engineering, Zhejiang University, Hangzhou, Zhejiang 310058 3 School of Management, University of Chinese Academy of Sciences, Beijing, 100190, China

Received  August 2014 Revised  January 2015 Published  April 2015

In this paper, we study the polyhedral cone constrained homogeneous quadratic programming problem and provide an equivalent linear conic reformulation. Based on a union of second-order cones which covers the polyhedral cone, a sequence of computable linear conic programming problems are constructed to approximate the linear conic reformulation. The convergence of the sequential solutions is guaranteed as the number of second-order cones increases such that the union of the second-order cones gets close to the polyhedral cone. In order to relieve the computational burden and improve the efficiency, an adaptive scheme and valid inequalities derived by the reformulation-linearization technique are added to the proposed algorithm. Finally, the numerical results demonstrate the effectiveness of the algorithm.
Citation: Ye Tian, Qingwei Jin, Zhibin Deng. Quadratic optimization over a polyhedral cone. Journal of Industrial & Management Optimization, 2016, 12 (1) : 269-283. doi: 10.3934/jimo.2016.12.269
##### References:

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##### References:
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