鲁棒灵敏度分析问题和二次约束二次规划问题的性质及其计算方法,通过线性锥规划理论的研究,建立线性锥规划模型,给出最优性条件和求解全局最优解或近似全局最优解的算法及收敛性分析。在国内外学术刊物发表论文60余篇,出版专著1部,教材7部。
[1] Cheng Lu, Shu-Cherng Fang, Qinwei Jin, Zhenbo Wang and Wenxun Xing. KKT solution and conic relaxation for solving quadratically constrained quadratic programming problems, SIAM J. Optimization, 21: 1475-1490, 2011.
[2] Wenxun Xing, Shu-Cherng Fang, Ruey-Lin Sheu and Ziteng Wang. A canonical dual approach for solving linearly constrained quadratic programs. European Journal of Operational Research, 218: 21-27, 2012.
[3] Jing Zhou, Shu-Cherng Fang and Wenxun Xing, Conic approximation to quadratic optimization with linear complementarity constraints, Comput Optim Appl, 66:97–122, 2017.
[4] Ruotian Gao and Wenxun Xing, Robust sensitivity analysis for linear programming with ellipsoidal perturbation. J. Industrial and Management Optimization, 16(4), 2029-2044, 2020
[5] Shan Jiang, Shu-Cherng Fang, Tiantian Nie and Wenxun Xing, A gradient descent based algorithm for lp minimization, European Journal of Operational Research 283, 47-56, 2020.