@article{jiang_fang_nie_xing_2020, title={A gradient descent based algorithm for ℓp minimization}, volume={283}, ISSN={0377-2217}, url={http://dx.doi.org/10.1016/j.ejor.2019.11.051}, DOI={10.1016/j.ejor.2019.11.051}, abstractNote={In this paper, we study the linearly constrained ℓp minimization problem with p ∈ (0, 1). Unlike those known works in the literature that propose solving relaxed ϵ-KKT conditions, we introduce a scaled KKT condition without involving any relaxation of the optimality conditions. A gradient-descent-based algorithm that works only on the positive entries of variables is then proposed to find solutions satisfying the scaled KKT condition without invoking the nondifferentiability issue. The convergence proof and complexity analysis of the proposed algorithm are provided. Computational experiments support that the proposed algorithm is capable of achieving much better sparse recovery in reasonable computational time compared to state-of-the-art interior-point based algorithms.}, number={1}, journal={European Journal of Operational Research}, publisher={Elsevier BV}, author={Jiang, Shan and Fang, Shu-Cherng and Nie, Tiantian and Xing, Wenxun}, year={2020}, month={May}, pages={47–56} }
 @article{qian_fang_huang_nie_wang_2019, title={Bidding Decisions with Nonequilibrium Strategic Thinking in Reverse Auctions}, volume={28}, ISSN={0926-2644 1572-9907}, url={http://dx.doi.org/10.1007/s10726-019-09624-7}, DOI={10.1007/s10726-019-09624-7}, number={4}, journal={Group Decision and Negotiation}, publisher={Springer Science and Business Media LLC}, author={Qian, Xiaohu and Fang, Shu-Cherng and Huang, Min and Nie, Tiantian and Wang, Xingwei}, year={2019}, month={Jun}, pages={757–786} }
 @article{li_fang_huang_nie_2016, title={An enhanced logarithmic method for signomial programming with discrete variables}, volume={255}, ISSN={0377-2217}, url={http://dx.doi.org/10.1016/j.ejor.2016.05.063}, DOI={10.1016/j.ejor.2016.05.063}, abstractNote={Signomial programming problems with discrete variables (SPD) appear widely in real-life applications, but they are hard to solve. This paper proposes an enhanced logarithmic method to reformulate the SPD problem as a mixed 0-1 linear program (MILP) with a minimum number of binary variables and inequality constraints. Both of the theoretical analysis and numerical results strongly support its superior performance to other state-of-the-art linearization methods. We also extend the proposed method to linearize some more complicated problems involving product and fractional terms in discrete and continuous variables.}, number={3}, journal={European Journal of Operational Research}, publisher={Elsevier BV}, author={Li, Han-Lin and Fang, Shu-Cherng and Huang, Yao-Huei and Nie, Tiantian}, year={2016}, month={Dec}, pages={922–934} }
 @article{nie_fang_deng_lavery_2016, title={On linear conic relaxation of discrete quadratic programs}, volume={31}, ISSN={1055-6788 1029-4937}, url={http://dx.doi.org/10.1080/10556788.2015.1134528}, DOI={10.1080/10556788.2015.1134528}, abstractNote={A special reformulation-linearization technique based linear conic relaxation is proposed for discrete quadratic programming (DQP). We show that the proposed relaxation is tighter than the traditional positive semidefinite programming relaxation. More importantly, when the proposed relaxation problem has an optimal solution with rank one or two, optimal solutions to the original DQP problem can be explicitly generated. This rank-two property is further extended to binary quadratic optimization problems and linearly constrained DQP problems. Numerical results indicate that the proposed relaxation is capable of providing high quality and robust lower bounds for DQP.}, number={4}, journal={Optimization Methods and Software}, publisher={Informa UK Limited}, author={Nie, Tiantian and Fang, Shu-Cherng and Deng, Zhibin and Lavery, John E.}, year={2016}, month={Jan}, pages={737–754} }