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January  2016, 12(1): 317-336. doi: 10.3934/jimo.2016.12.317

## An alternating direction method for solving a class of inverse semi-definite quadratic programming problems

 1 Institute of Operations Research and Control Theory, School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China, China 2 School of Transportation and Logistics, Faculty of Infrastructure Engineering, Dalian University of Technology, Dalian 116024, China

Received  April 2013 Revised  January 2015 Published  April 2015

In this paper, we propose an alternating-direction-type numerical method to solve a class of inverse semi-definite quadratic programming problems. An explicit solution to one direction subproblem is given and the other direction subproblem is proved to be a convex quadratic programming problem over positive semi-definite symmetric matrix cone. We design a spectral projected gradient method for solving the quadratic matrix optimization problem and demonstrate its convergence. Numerical experiments illustrate that our method can solve inverse semi-definite quadratic programming problems efficiently.
Citation: Yue Lu, Ying-En Ge, Li-Wei Zhang. An alternating direction method for solving a class of inverse semi-definite quadratic programming problems. Journal of Industrial & Management Optimization, 2016, 12 (1) : 317-336. doi: 10.3934/jimo.2016.12.317
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