Globally solving quadratic programs with convex objective and complementarity constraints via completely positive programming
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2017
doi:10.3934/jimo.2017064 Abstract
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ZhiBin Deng  School of Economics and Management, University of Chinese Academy of Sciences, Key Laboratory of Big Data Mining and Knowledge Management, Chinese Academy of Sciences, Beijing 100190, China (email)
Ye Tian  School of Business Administration, Southwestern University of Finance and Economics, Chengdu, 611130, China (email)
Cheng Lu  School of Economics and Management, North China Electric Power University, Beijing 102206, China (email)
WenXun Xing  Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China (email)
1 
L. Bai, J. E. Mitchell and J.S. Pang, On convex quadratic programs with linear complementarity constraints, Computational Optimization and Applications, 54 (2013), 517554. 

2 
J. Beasley, ORLibrary: distributing test problems by electronic mail, Journal of the Operational Research Society, 41 (1990), 10691072. 

3 
A. Billionnet, S. Elloumi and M.C. Plateau, Improving the performance of standard solvers for quadratic 01 programs by a tight convex reformulation: The QCR method, Discrete Applied Mathematics, 157 (2009), 11851197. 

4 
S. Burer, On the copositive representation of binary and continuous nonconvex quadratic programs, Mathematical Programming, 120 (2009), 479495. 

5 
S. Burer, Optimizing a polyhedralsemidefinite relaxation of completely positive programs, Mathematical Programming Computation, 2 (2010), 119. 

6 
Y.L. Chang, J.S. Chen and J. Wu, Proximal point algorithm for nonlinear complementarity problem based on the generalized fischerburmeister merit function, Journal of Industrial and Management Optimization, 9 (2013), 153169. 

7 
P. J. Dickinson and L. Gijben, On the computational complexity of membership problems for the completely positive cone and its dual, Computational Optimization and Applications, 57 (2014), 403415. 

8 
M. C. Ferris and J. S. Pang, Engineering and economic applications of complementarity problems, SIAM Review, 39 (1997), 669713. 

9 
C. Hao and X. Liu, A trustregion filtersqp method for mathematical programs with linear complementarity constraints, Journal of Industrial and Management Optimization, 7 (2011), 10411055. 

10 
T. Hoheisel, C. Kanzow and A. Schwartz, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints, Mathematical Programming, 137 (2013), 257288. 

11 
J. Hu, J. E. Mitchell, J.S. Pang, K. P. Bennett and G. Kunapuli, On the global solution of linear programs with linear complementarity constraints, SIAM Journal on Optimization, 19 (2008), 445471. 

12 
X. X. Huang, D. Li and X. Q. Yang, Convergence of optimal values of quadratic penalty problems for mathematical programs with complementarity constraints, Journal of Industrial and Management Optimization, 2 (2006), 287296. 

13 
H. Jiang and D. Ralph, QPECgen, a MATLAB generator for mathematical programs with quadratic objectives and affine variational inequality constraints, Computational Optimization and Applications, 13 (1999), 2559. 

14 
J. J. Júdice and A. Faustino, The linearquadratic bilevel programming problem, Information Systems and Operational Research, 32 (1994), 8798. 

15 
S. Kim, M. Kojima and K.C. Toh, A lagrangiandnn relaxation: A fast method for computing tight lower bounds for a class of quadratic optimization problems, Mathematical Programming, 156 (2016), 161187. 

16 
S. Leyffer, MacMPEC: AMPL collection of mathematical problems with equilibrium constraints, 2015, URL http://wiki.mcs.anl.gov/leyffer/index.php/MacMPEC. 

17 
C. Lu, W. Xing, S.C. Fang and Z. Deng, Doubly nonnegative relaxation solution based branchandbound algorithms for mixed integer quadratic programs, Working paper. 

18 
C. Lu and X. Guo, Convex reformulation for binary quadratic programming problems via average objective value maximization, Optimization Letters, 9 (2015), 523535. 

19 
O. Mangasarian and S. Fromovitz, The Fritz John necessary optimality conditions in the presence of equality and inequality constraints, Journal of Mathematical Analysis and Applications, 17 (1967), 3747. 

20 
P. Pardalom and S. Jha, Complexity of uniqueness and local search in quadratic 01 programming, Operations Research Letters, 11 (1992), 119123. 

21 
T. Rockafellar, Convex Analysis, Princeton University Press, Princeton, N.J., 1970. 

22 
J. Sun and S. Zhang, A modified alternating direction method for convex quadratically constrained quadratic semidefinite programs, European Journal of Operational Research, 207 (2010), 12101220. 

23 
Z. Wen, D. Goldfarb and W. Yin, Alternating direction augmented lagrangian methods for semidefinite programming, Mathematical Programming Computation, 2 (2010), 203230. 

24 
X.Y. Zhao, D.F. Sun and K.C. Toh, A NewtonCG augmented Lagrangian method for semidefinite programming, SIAM Journal on Optimizaton, 20 (2010), 17371765. 

25 
J. Zhou, S.C. Fang and W. Xing, Conic approximation to quadratic optimization with linear complementarity constraints, Computational Optimization and Applications, 66 (2017), 92122. 

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