长期以来，万中教授对大规模优化问题、多态不确定优化问题、多准则群决策理论开展了较深入研究，提出了新型谱共轭梯度算法、新型非单调线搜索规则、多准则群决策权重优化模型、以及处理多态不确定性优化问题或者均衡问题的柔性优化方法等，发表了一系列研究成果。具体说来，主要成果可概述为以下几点：
(1) 在多态不确定性规划理论与算法研究方面
我们基于模型化和数值计算技术，对不确定环境下的工程与管理优化问题开展了长期、较系统的研究。主要代表性研究成果有: （a）对多生产商和销售商的供应链管理中的分散式决策问题，构建了多态不确定均衡模型。该模型假设消费者需求是连续性随机变量，库存成本和交易成本处理是模糊参数，刻画了各决策主体之间复杂策略博弈；提出了柔性优化方法处理该模型的多态不确定性，并得到该模型的确定型对等式；最后基于本项目团队提出的修正Jacobian部分磨光算法对模型进行数值求解。研究成果发表在《Appl. Math. Modelling》上 [Wan, et al., 2018]。(b) 在连续性随机需求条件下，构建了全球供应链管理问题的集中式决策优化模型；该模型把中间产品的转移价格，零售价格和订货量均作为系统的内生变量，实现了全球供应链企业最大化税后利润；基于期望方法和模型的解析性质(如复杂目标函数和约束函数的梯度信息)，开发了求解这类模型的高效算法。大量的场景分析和数值实验揭示了模型的许多管理实践启示。该部分成果发表在《Appl. Math. Modelling》和《Operational Research》上 [Zhang et al., 2018；Zhang et al., 2016]。(c) 针对实际工程设计环境中存在诸多不确定性因素，我们首次给出了“多态不确定优化问题”的概念以刻画模型参数的多态不确定性属性[Wan et al., 2014b]；构建建立了V带传动载荷极大化和疲劳寿命极大化问题的多态不确定性数学规划模型；提出了统一的柔性优化方法，把含多态不确性参数的优化问题转变成确定性模型以寻求一定满意度下的最优解。 开发了求解多态非线性不确定优化问题的基于两步的交互式抽样算法和基于可能度方法的抽样算法。部分成果发表在《Optimization and Engineering》、英国工程师协会会刊《Journal of Mechanical Engineering Science》和《Journal of Industrial and Management Optimization》上。（d）构建了同时含有广告和定价策略优化的供货商管理库存问题(VMI)的随机双层规划模型，该模型中的需求不是像已有文献假设为决策系统的外生参数，而是处理成既依赖于决策变量(价格和广告投入)，又依赖市场波动的连续性随机函数。对于所建立的随机双层规划模型，我们首先基于期望方法和KKT条件将原问题转化成互补约束优化问题(MPCC)，再基于部分磨光技术将MPCC转化成普通的光滑优化问题求解。敏感性分析揭示了该模型对管理实践的指导价值，研究成果2017年发表在《The ANZIAM Journal》上。
此外，我们在不确定性规划理论与算法方面做了以下工作：a)提出了处理随多态不确定优化问题的满意度方法。同已有方法（如期望值方法、机会约束规划方法）相比，该方法不需要假设随机参数服从的分布函数，而是直接根据已有数据的数字特征处理该类问题，并已初步应用到处理氧化铝烧结法配料优化问题[Wan et al., 2009；Jiang and Wan, 2013]。 b）以证券组合优化问题为研究背景，提出了求解随机优化问题的期望-方差综合法[Wan et al., 2010]。该方法将含有利润最大化和风险最小化的双目标问题约束优化问题转化成一类无约束优化问题进行研究，并证明了所对应的无约束优化问题是一个分片凸二次函数的极小化问题；基于共轭梯度法和罚方法开发了高效交互式算法。c）提出了处理多态不确定优化问题的区间解的柔性优化方法[Wan et al., (2013a)]。
代表性成果：
Ø [Wan, et al., 2018] Zhong Wan, Hao Wu, Lin Dai，A polymorphic uncertain equilibrium model and its deterministic equivalent formulation for decentralized supply chain management, Applied Mathematical Modelling, 58：281-299, 2018.
Ø [Zhang， et al., 2018] Xinbo Zhang, Shuai Huang, Zhong Wan (通讯作者), Stochastic programming approach to global supply chain management under random additive demand, Oper Res Int J , 18(2):389–420, 2018.
Ø [Zhang， et al., 2016] Xinbo Zhang, Shuai Huang, Zhong Wan (通讯作者), Optimal pricing and ordering in global supply chain management with constraints under random demand, Appl. Math. Modelling，40:10105-10130, 2016.
Ø [Wan et al., 2014b] Zhong Wan, Shaojun Zhang, , Kok Lay Teo, Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving, Optimization and Engineering, 15:267-292, 2014.
Ø [Zhang and Wan, 2012] Shaojun Zhang, Zhong Wan(通讯作者), Polymorphic uncertain nonlinear programming model and algorithm for maximizing the fatigue life of V-belt drive, Journal of Industrial and Management Optimization, 8(2):493-505, 2012. （JCR二区）
Ø [Wan， et al.， 2012a] Zhong Wan, ShaoJun Zhang, Kok-Lay Teo . Two-step based sampling method for maximizing the capacity of V-belt driving in polymorphic uncertain environment, P I MECH ENG C- Proceedings of the institution of mechanical engineers part c-journal of mechanical engineering science, 226 (1): 177-191. 2012
Ø [Wan，et al., 2010] Zhong Wan*, Aiyun Hao, Fuzheng Meng, ZhaoMing Hu, Hybrid Method for a Class of Stochastic Bi-criteria Optimization Problems, Journal of Inequalities and Applications , 2010:1-12, 2010.
Ø [Wan, et al., 2009] Zhong Wan, Koklay Teo, Lingshuang Kong and Chunhua Yang. A class of mix design problems: formulation, solution methods and applications. The ANZIAM Journal, 50:455-474, 2009.
Ø [Wan, et al., 2013a] Zhong Wan, Shaojun Zhang, Yanju Zhou. Interval solution for nonlinear programming of maximizing the fatigue life of V-belt under polymorphic uncertain environment, Mathematical Problems in Engineering, Vol.2013, Article ID 712825,9 pages, http://dx.doi.org/10.1155/2013/712825
Ø [Jiang and Wan, 2013] Huabin Jiang, Zhong Wan (通讯作者), Polymorphic Uncertain Optimization to Renewable Energy Planning in the City Cluster, International Journal of Applied Mathematics & Statistics, 50(20): 224-237, 2013.
[Zhang, et al., 2014] Xinbo Zhang, Feng Zhang, Xiaohong Chen, and Zhong Wan (通讯作者), Polymorphic uncertain linear programming for generalized production planning problems, Journal of Optimization, vol. 2014, Article ID 896756, 10 pages, 2014.
(2) 在复杂非线性优化理论和高效算法研究方面
我们对约束或无约束优化、无限维约束优化、非线性方程组、全局优化等进行了深入的研究，并在国内外许多重要学术期刊发表高水平论文40余篇。主要创新性成果有：
a) 提出了寻求复杂优化问题的新型非单调线搜索技术。现有的几种经典单调或者非单调线搜索。我们一方面在较弱的条件下建立了基于该线搜索技术算法的全局收敛性和局部R-线性收敛性理论，另一方面又基于大量大规模基准测试问题测试证明了(1)和(2)在求解大规模复杂优化问题时更好的数值效率[J. Comput. Appl. Math.,2018, 586-604]。
b) 提出了几类新型共轭梯度方法和谱共轭梯度方法，并分别建立了它们的全局和局部收敛性理论，其数值效率在求解大量的基准测试问题中得到证实[Appl. Numer. Math., 92:70-81; JOTA, 157: 820-842; Appl. Math. Letter, 24:16-22; Optimization, 64: 2679-2691].
c) 提出了求解大规模非线性方程组高效数值解法。对非线性局部李普希兹连续方程组，提出了新型非单调谱残量方法，该方法不需要计算导数，其搜索步长是极小化近似割线方程的残量问题的最优解，在弱的条件下建立的算法的全局收敛性理论，且具有更高的数值效率[J. Comput. Appl. Math., 82-101]。对光滑非线性方程组开发了非单调修正BFGS算法[Optim. Letters, 8: 1845-1860].
d) 提出了新型自适应Barzilai-Borwein（BB）步长，该步长能够根据当前算法的迭代点处两种经典的BB步长的优势来计算自适应计算它们的组合权重以得到新步长。将该步长与计算成本最低的最速下降法结合，我们建立了其全局收敛性和R-线性收敛性。数值结果表明这种方法在求解病态或者大规模问题时具有更好的数值性能[ANZIAM Journal, online first]。
此外， 我们还在均衡约束优化、积分型无限维二次规划、全局优化、互补问题研究方面发表了一系列研究成果：[SIAM J. Optim., 15: 275-302; J. Comput. Appl. Math., 286: 158-171; Appl. Math. Letters, 20: 676-680; SCIENCE CHINA(E)，Technological Sciences, 54:140-147; Numer. Functional Analysis Optim.，27: 485-495 ; J. Industrial and Management Optim., 4 (2): 271-285; Proc IMechE Part C: J Mechanical Engineering Science, 227: 1804–1817; ANZIAM Journal, 56: 299-315].
代表性成果：
Ø [Huang et al., 2018] Shuai Huang, Zhong Wan (通讯作者), Jing Zhang (通讯作者). An extended nonmonotone line search technique for large-scale unconstrained optimization, Journal of Computational and Applied Mathematics, 330:586-604, 2018.
Ø [Huang and Wan, 2017] Shuai Huang, Zhong Wan (通讯作者). A new nonmonotone spectral residual method for nonsmooth nonlinear equations, Journal of Computational and Applied Mathematics. 313( 15) : 82-101, 2017.
Ø [Deng and Wan, 2015] Songhai Deng, Zhong Wan (通讯作者). A three-term conjugate gradient algorithm for large-scale unconstrained optimization problems, Applied Numerical Mathematics, 92: 70-81, 2015.
Ø [Huang, et al., 2015] Shuai Huang, Zhong Wan (通讯作者)，Xiaohong Chen. A new nonmonotone line search technique for unconstrained optimization, Numerical Algorithms, 68(4): 671-689, 2015.
Ø [Wan, et al., 2015c] Zhong Wan, Min Yuan, Chang Wang. A partially smoothing Jacobian method for nonlinear complementarity problems with P-0 function, Journal of Computational and Applied Mathematics, 286: 158-171, 2015.
Ø [Deng and Wan, 2012)] Songhai Deng, Zhong Wan(通讯作者). An improved spectral conjugate gradient algorithm for nonconvex unconstrained optimization problems, Journal of Optimization Theory and Applications, 157(3): 820-842, 2012.
Ø [Wan, et al., 2011] Zhong Wan, Yang Zhanlu, Wang Yalin, New spectral PRP conjugate gradient method for unconstrained optimization, Applied Mathematics Letters, 24(1): 16-22, 2011.
Ø [Qi, et al., 2005]L.Qi, Zhong Wan, Yuefei,Yang. Global minimization of normal quartic polynomials based on the descent directions，SIAM on Optim., 15 (1) : 275-302, 2005.
Ø [Wan, et al., 2007] Zhong Wan, Song Yi Wu, Kok Lay Teo. Some Properties on Quadratic Infinite Programs of Integral Type, Applied Mathematics Letter, 20: 676-680, 2007.
Ø [Wan, 2002] Zhong Wan. Further investigation on feasibility of mathematical programs with equilibrium constraints. Computer and Mathematical Applications，44: 7-11, 2002.
Ø [Chen and Wan, 2015] Yu Chen, Zhong Wan(通讯作者). A Locally Smoothing Method for Mathematical Programs with Complementarity Constraints, The ANZIAM Journal, 56（3）: 299-315, 2015.
Ø [Deng and Wan, 2015] Songhai Deng, Zhong Wan (通讯作者). An improved three-term conjugate gradient algorithm for solving unconstrained optimization problems, Optimization, 64(12): 2679-2691, 2015.
Ø [Wan, et al., 2014a] Zhong Wan, Kok lay Teo, Xianlong Shen. New BFGS method for unconstrained optimization problem based on modified Armijo line search, Optimization， 63（2）： 285-304，2014
Ø [Wan, et al., 2014] Zhong Wan, Yu Chen, Shuai Huang, Dong Dong Feng. A modified nonmonotone BFGS algorithm for solving smooth nonlinear equations, Optimization Letters, 8:1845–1860, 2014 .
Ø [Huang, et al., 2013] Shuai Huang, Zhong Wan(通讯作者), Songhai Deng. A modified projected conjugate gradient method for unconstrained optimization problems, The ANZIAM Journal, 54(3): 143-152, 2013.
Ø [Zhang, et al., 2011] Shaojun Zhang, Zhong Wan(通讯作者)，Liu GuangLian. Global optimization design method for maximizing the capacity of V-belt drive，SCIENCE CHINA，Technological Sciences, 54(1):140-147, 2011.
Ø [Wan, et al., 2011] Zhong Wan, Chaoming Hu， Zhanlu Yang. A spectral PRP conjugate gradient methods for nonconvex optimization problem based on modified line search, Discrete and Continuous Dynamical Systems- B, 16(4):1153-1169, 2011.
Ø [Wan and Yang, 2008] Zhong Wan，Chunhua Yang. New approach to global minimization of normal multivariate polynomial based on tensor，Journal of Industrial and Management Optimization, 4 (2):271-285，2008.
Ø [Wan, et al.,2012b] Zhong Wan, ShaoJun Zhang, Xiaohong Chen. Formulation for an optimal design problem of spur gear drive and its global optimization, Proc IMechE Part C: J Mechanical Engineering Science, 227(8): 1804–1817, 2012.
Ø [Chen and Wan, 2018] Yu Chen, Zhong Wan(通讯作者). A new smoothing method for mathematical programs with complementarity constraints based on logarithm-exponential function, Math. Problems in Engineering, 2018, Article ID 5056148, 2018.
Ø [Li and Wan, 2018] Ting Li, Zhong Wan(通讯作者). New adaptive Barzilar-Borwein step size and its application in solving large scale optimization problems, The ANZIAM Journal, (online first, 2018, https://doi.org/10.1017/S1446181118000263).
Ø [Wan, et al., 2016] Zhong Wan, Weiyi Liu, Chang Wang. A modified spectral conjugate gradient projection method for solving nonlinear monotone equations. Pacific Journal of Optimization, 12(3):603-622, 2016.
Ø [Chen, et al., 2016b] Yu Chen, Shuai Huang, Zhong Wan (通讯作者). A strong convergent smoothing regularization method for mathematical programs with complementarity constraints, Pacific Journal of Optimization, 12(3):497-519, 2016.
Ø [Wan, et al., 2015a] Zhong Wan, Yu Chen and Xiaodong Zheng，Solution method of optimisation problem based on a modified Armijo-type line search，International Journal of Computational Science and Engineering, 11(3): 322-329, 2015.
Ø [Wan, et al., 2012] Zhong Wan, Shuai Huang, Xiaodong Zheng. New cautious BFGS algorithm based on modified Armijo-type line search, Journal of Inequalities and Applications 2012, 2012:241,doi:10.1186/1029-242X-2012-241.
Ø [Wan and Wang, 2006] Zhong Wan, Yi Ju Wang, Convergence of an inexact smoothing method for mathematical programs with equilibrium constraints, Numerical Functional Analysis and Optimization, 27(3-4): 485-495, 2006.
Ø [Jiang, et al., 2012] Huabin, Jiang, Songhai Deng, Xiaodong Zheng, Zhong Wan(通讯作者) . Global convergence of a modified spectral conjugate gradient method, Journal of Applied Mathematics, Vol. 2012, Article ID 641276, doi:10.1155/2012/641276
Ø [Wan et al. 2015b] Zhong Wan, HuanHuan Li, and Shuai Huang. A Smoothing Inexact Newton Method for Nonlinear Complementarity Problems. Abstract and Applied Analysis. 2015, Article ID 731026, 1-12. doi:10.1155/2015/731026.
Ø [Hu and Wan, 2013] Chaoming Hu, Zhong Wan(通讯作者). An extended spectral conjugate gradient method for unconstrained optimization problems, British Journal of Mathematics & Computer Science, 3(2), 86-98, 2013.
Ø [Deng, et al., 2013] Songhai Deng, Xiaohong Chen, Zhong Wan(通讯作者). Analysis on an improved global convergence for a spectral conjugate gradient method, International Journal of Applied Mathematics & Statistics, 31(1):20-26, 2013.
Ø [Wan, et al., 2012] Zhong Wan, XiaoDong Zheng, YunYun Fei, Songhai Deng. Modified Armijo-type line search strategy and its applications in Newton method for unconstrained optimization, International Journal of Applied Mathematics & Statistics, 29(5):116-125, 2012.
(3) 在多准则群决策理论的研究方面
a) 我们依据多属性群(评判)数据，构造的数据驱动的准则权重和专家权重选择的Min-Max优化模型[Chen et al., 2015]。对于准则权重，该Min-Max优化模型基于“同一专家的准则权重具有一致性”这种共识来构建，而不是像现有成果中按“准则的区分度”来优化权重。
b) 提出了非线性贡献分配模型，比已有文献中的线性模型更合理，且具有更广泛的应用性。
c) 提出了判别矩阵的新的不一致性度量指标[Chen and Wan, 2016]。该成果已被2018年发表在权威期刊《International Journal of General Systems》（Brunelli，47(8)：751-771）上综述论文作为主要方法之一引用。
d) 提出了多属性席位分配问题的参数化整数规划模型，提出了部分解决了“Alabama”悖论的方法[Wan, 2006]。
代表性成果：
Ø [Chen and Wan, 2016] Ming Chen, Zhong Wan(通讯作者). New Nonlinear Metrics Model for Information of Individual Research Output and Its Applications. Mathematical and Computational Applications. 21(3):26. 2, 2016.
Ø [Chen, et al., 2015] Ming Chen, Zhong Wan(通讯作者), Xiaohong Chen. New Min-Max Approach to Optimal Choice of the Weights in Multi-Criteria Group Decision-Making Problems，Applied Sciences-Basel, 5(4): 998-1015, 2015.
Ø [Wan, et al., 2013] Zhong Wan, Ming Chen, Ling Zhang. New consistency index for comparison matrices and its properties, International Journal of Applied Mathematics & Statistics, 42(12): 206-218, 2013.
Ø [Wan, 2006] Zhong Wan, Parameterized integer programming models for multi-factor representative apportionment, Soc. Sci. J., 43（2）:259-272, 2006.
(4) 在工程与管理优化及应用研究方面
a) 对机械工程中非常重要的传动系统设计优化问题开展了深入研究，主要学术贡献包括提出了带传动和直齿传动系统设计全局优化算法[Zhang, et al., 2011; Wan, et al.,2012b]；提出了多态不确定环境下的带传动系统设计优化的问题的一系列柔性优化方法[Zhang and Wan, 2012; Wan, et al., 2012a; Wan, et al., 2013a; Wan, et al., 2014b]。
b) 对固废管理优化、路径规划、和供应链管理优化问题开展了较广泛深入的研究，近年来的主要学术贡献有：(i)在多态不确定性环境下, 构建了三级供应链管理分散式决策博弈模型，开发了基于部分磨光的Jacobian牛顿类算法[Wan, et al., 2018]；（ii）构建了区域城市矿产开发利用问题的多目标分片光滑的混合整数非线性优化模型[Wu and Wan, 2018]。该模型首次将各类城市矿产回购价格和产能调整量作为系统的内生变量，不但实现了总的回收利润和生态效益极大化，也实现了产能调整可能带来的社会负面效应最小化. 模型采用基于变量替换技术和正交试验设计的混合元启发式算法进行求解，场景分析揭示了模型对管理实践的指导意义；(iii) 考虑随机需求和转移价格，构建了全球供应链管理集中式决策优化模型，基于模型梯度信息开发了高效的求解算法[Zhang et al., 2016]；(iv) 考虑依赖广告-价格的随机需求下，构建了供货商管理库存双层优化模型，开发了基于模型梯度信息开发了高效的求解算法[Li and Wan, 2018]。
代表性成果:
Ø [Wan, et al., 2018] Zhong Wan, Hao Wu, Lin Dai. A polymorphic uncertain equilibrium model and its deterministic equivalent formulation for decentralized supply chain management, Applied Mathematical Modelling, 58：281-299, 2018.
Ø [Wan, et al., 2018] Zhong Wan, Jie Guo, Jingjing Liu, Weiyi Liu. A modified spectral conjugate gradient projection method for signal recovery, Signal Image and Video Processing, 12（8）：1455–1462, 2018.
Ø [Wu and Wan, 2018] Hao Wu, Zhong Wan(通讯作者). A multiobjective optimization model and an orthogonal design-based hybrid heuristic algorithm for regional urban mining management problems, Journal of the Air & Waste Management Association, 68(2): 146-169, 2018.
Ø [Li, et al., 2018] Jiaoyan Li, Xiao Hu, Zhong Wan(通讯作者). An integrated bi-objective optimization model and improved genetic algorithm for vehicle routing problems with temporal and spatial constraints, Journal of Industrial and Management Optimization, 2018, doi:10.3934/jimo.2018200
Ø [Li and Wan, 2018] Yinxue Li, Zhong Wan(通讯作者). Bi-level programming approach to optimal strategy for VMI problems under random demand, The ANZIAM Journal, 59(2):247-270，2017.
Ø [Zhang, et al., 2016] Xinbo Zhang, Shuai Huang, Zhong Wan (通讯作者). Optimal pricing and ordering in global supply chain management with constraints under random demand, Appl. Math. Modelling，40 : 10105-10130, 2016.
Ø [Chen, et al., 2016a] XinRan Chen, Yongmei Liu, Zhong Wan (通讯作者). Optimal decision-making for the online and offline retailers under BOPS model, The ANZIAM Journal, 58(2)：187-208, 2016.
Ø [Zhang, et al., 2011] Shaojun Zhang, Zhong Wan (通讯作者)，Liu GuangLian. Global optimization design method for maximizing the capacity of V-belt drive，SCIENCE CHINA，Technological Sciences, 54(1):140-147, 2010.
Ø [Wan, et al.,2012b] Zhong Wan(通讯作者), ShaoJun Zhang, Xiaohong Chen. Formulation for an optimal design problem of spur gear drive and its global optimization, Proc IMechE Part C: J Mechanical Engineering Science, 227(8): 1804–1817, 2012.
Ø [Wan, et al., 2009] Zhong Wan, ShaoJun Zhang and Yalin Wang. Penalty Algorithm Based on Conjugate Gradient Method for Solving Portfolio Management Problem, J. Inequalities and Applications, vol. 2009, Article ID 970723, 16 pages, 2009.
Ø [Li, et al.，2018] Jiaoyan Li, Xiao Hu，Zhong Wan(通讯作者). An integrated bi-objective optimization model and improved genetic algorithm for vehicle routing problems with temporal and spatial constraints, J. Industrial and Management Optimization, doi: 10.3934/jimo.2018200, 2018.