# American Institute of Mathematical Sciences

October  2009, 5(4): 881-892. doi: 10.3934/jimo.2009.5.881

## New sufficient global optimality conditions for linearly constrained bivalent quadratic optimization problems

 1 LMIB of the Ministry of Education, School of Mathematics and System Sciences, Beihang University, Beijing, 100191, China

Received  October 2008 Revised  June 2009 Published  August 2009

In this article, we obtain new sufficient global optimality conditions for bivalent quadratic optimization problems with linearly (equivalent and inequivalent) constraints, by exploring the local optimality condition. The global optimality condition can be further simplified when applied to special cases such as the $p$-dispersion-sum problem and the quadratic assignment problem.
Citation: Yong Xia. New sufficient global optimality conditions for linearly constrained bivalent quadratic optimization problems. Journal of Industrial & Management Optimization, 2009, 5 (4) : 881-892. doi: 10.3934/jimo.2009.5.881
 [1] Shu-Cherng Fang, David Y. Gao, Ruey-Lin Sheu, Soon-Yi Wu. Canonical dual approach to solving 0-1 quadratic programming problems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 125-142. doi: 10.3934/jimo.2008.4.125 [2] Cheng Lu, Zhenbo Wang, Wenxun Xing, Shu-Cherng Fang. Extended canonical duality and conic programming for solving 0-1 quadratic programming problems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 779-793. doi: 10.3934/jimo.2010.6.779 [3] Jing Zhou, Dejun Chen, Zhenbo Wang, Wenxun Xing. A conic approximation method for the 0-1 quadratic knapsack problem. Journal of Industrial & Management Optimization, 2013, 9 (3) : 531-547. doi: 10.3934/jimo.2013.9.531 [4] Ye Tian, Cheng Lu. Nonconvex quadratic reformulations and solvable conditions for mixed integer quadratic programming problems. Journal of Industrial & Management Optimization, 2011, 7 (4) : 1027-1039. doi: 10.3934/jimo.2011.7.1027 [5] Zhenbo Wang, Shu-Cherng Fang, David Y. Gao, Wenxun Xing. Global extremal conditions for multi-integer quadratic programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 213-225. doi: 10.3934/jimo.2008.4.213 [6] Lidan Li, Hongwei Zhang, Liwei Zhang. Inverse quadratic programming problem with $l_1$ norm measure. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-13. doi: 10.3934/jimo.2019061 [7] Ziye Shi, Qingwei Jin. Second order optimality conditions and reformulations for nonconvex quadratically constrained quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (3) : 871-882. doi: 10.3934/jimo.2014.10.871 [8] Wan Nor Ashikin Wan Ahmad Fatthi, Adibah Shuib, Rosma Mohd Dom. A mixed integer programming model for solving real-time truck-to-door assignment and scheduling problem at cross docking warehouse. Journal of Industrial & Management Optimization, 2016, 12 (2) : 431-447. doi: 10.3934/jimo.2016.12.431 [9] Jing Quan, Zhiyou Wu, Guoquan Li. Global optimality conditions for some classes of polynomial integer programming problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 67-78. doi: 10.3934/jimo.2011.7.67 [10] Zhiguo Feng, Ka-Fai Cedric Yiu. Manifold relaxations for integer programming. Journal of Industrial & Management Optimization, 2014, 10 (2) : 557-566. doi: 10.3934/jimo.2014.10.557 [11] Yasmine Cherfaoui, Mustapha Moulaï. Biobjective optimization over the efficient set of multiobjective integer programming problem. Journal of Industrial & Management Optimization, 2017, 13 (5) : 0-0. doi: 10.3934/jimo.2019102 [12] R. N. Gasimov, O. Ustun. Solving the quadratic assignment problem using F-MSG algorithm. Journal of Industrial & Management Optimization, 2007, 3 (2) : 173-191. doi: 10.3934/jimo.2007.3.173 [13] Kien Ming Ng, Trung Hieu Tran. A parallel water flow algorithm with local search for solving the quadratic assignment problem. Journal of Industrial & Management Optimization, 2019, 15 (1) : 235-259. doi: 10.3934/jimo.2018041 [14] Andrew E.B. Lim, John B. Moore. A path following algorithm for infinite quadratic programming on a Hilbert space. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 653-670. doi: 10.3934/dcds.1998.4.653 [15] Yanqin Bai, Chuanhao Guo. Doubly nonnegative relaxation method for solving multiple objective quadratic programming problems. Journal of Industrial & Management Optimization, 2014, 10 (2) : 543-556. doi: 10.3934/jimo.2014.10.543 [16] Paul B. Hermanns, Nguyen Van Thoai. Global optimization algorithm for solving bilevel programming problems with quadratic lower levels. Journal of Industrial & Management Optimization, 2010, 6 (1) : 177-196. doi: 10.3934/jimo.2010.6.177 [17] Songqiang Qiu, Zhongwen Chen. An adaptively regularized sequential quadratic programming method for equality constrained optimization. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019075 [18] Ailing Zhang, Shunsuke Hayashi. Celis-Dennis-Tapia based approach to quadratic fractional programming problems with two quadratic constraints. Numerical Algebra, Control & Optimization, 2011, 1 (1) : 83-98. doi: 10.3934/naco.2011.1.83 [19] Xiaoling Sun, Hongbo Sheng, Duan Li. An exact algorithm for 0-1 polynomial knapsack problems. Journal of Industrial & Management Optimization, 2007, 3 (2) : 223-232. doi: 10.3934/jimo.2007.3.223 [20] Yongjian Yang, Zhiyou Wu, Fusheng Bai. A filled function method for constrained nonlinear integer programming. Journal of Industrial & Management Optimization, 2008, 4 (2) : 353-362. doi: 10.3934/jimo.2008.4.353

2018 Impact Factor: 1.025

## Metrics

• PDF downloads (18)
• HTML views (0)
• Cited by (4)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]