动态规划在教学管理中的应用

本将动态规划理论应用于高校教学管理当中，得出了教学管理中重要的环一排课的最优策略。     

多周期公用工程系统运行的模型,优化方法与应用

针对多周期公用工程系统的运行优化问题，考虑了设备的启停费用的情况下。建立了混合整数非线性规划模型并证明了最优解的存在性。针对该运行优化问题本将其分解成若干子问题，然后利用改进的Hooke-Jeeves优化算法求解每个子问题。应用于具体实例，其数值结果与其它方法得到的相比。运行时间短，且更适合多周期公用工程问题的求解。     

直接求线性规划可行基的一种方法

本文给出直接求线性规划问题基可行解的一种简易方法,该方法既避免了引入人工变量,减少存储,一般又能较快地得到一个较好的基可行解.     

Minkowski-type and Alexandrov-Type Theorems for Polyhedral Herissons

Classical H. Minkowski theorems on existence and uniqueness of convex polyhedra with prescribed directions and areas of faces as well as the well-known generalization of H. Minkowski uniqueness theorem due to A.D. Alexandrov are extended to a class of nonconvex polyhedra which are called polyhedral herissons and may be described as polyhedra with injective spherical image.     

Analysis of a Duopoly Supply Chain and its Application in Electricity Spot Markets

This paper studies a supply chain consisting of two suppliers and one retailer in a spot market, where the retailer uses the newsvendor solution as its purchase policy, and suppliers compete for the retailer’s purchase. Since each supplier’s bidding strategy affects the other’s profit, a game theory approach is used to identify optimal bidding strategies. We prove the existence and uniqueness of a Nash solution. It is also shown that the competition between the supplier leads to a lower market clearing price, and as a result, the retailer benefits from it. Finally, we demonstrate the applicability of the obtained results by deriving optimal bidding strategies for power generator plants in the deregulated California energy market. Supported in part by RGC (Hong Kong) Competitive Earmarked Research Grants (CUHK4167/04E and CUHK4239/03E), a Distinguished Young Investigator Grant from the National Natural Sciences Foundation of China, and a grant from Hundred Talents Program of the Chinese Academy of Sciences.     

Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems. We first present a brief review of MILP and MINLP for the case when these problems are modeled with algebraic equations and inequalities. Since algebraic representations have some limitations such as difficulty of formulation and numerical singularities for the nonlinear case, we consider logic-based modeling as an alternative approach, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years. Solution strategies for GDP models are reviewed, including the continuous relaxation of the disjunctive constraints. Also, we briefly review a hybrid model that integrates disjunctive programming and mixed-integer programming. Finally, the global optimization of nonconvex GDP problems is discussed through a two-level branch and bound procedure.     

A new proof for Rockafellar's characterization of maximal monotone operators

We provide a new and short proof for Rockafellar's characterization of maximal monotone operators in reflexive Banach spaces based on S. Fitzpatrick's function and a technique used by R. S. Burachik and B. F. Svaiter for proving their result on the representation of a maximal monotone operator by convex functions.

     

A Hybrid Approach to Scheduling with Earliness and Tardiness Costs

A hybrid technique using constraint programming and linear programming is applied to the problem of scheduling with earliness and tardiness costs. The linear model maintains a set of relaxed optimal start times which are used to guide the constraint programming search heuristic. In addition, the constraint programming problem model employs the strong constraint propagation techniques responsible for many of the advances in constraint programming for scheduling in the past few years. Empirical results validate our approach and show, in particular, that creating and solving a subproblem containing only the activities with direct impact on the cost function and then using this solution in the main search, significantly increases the number of problems that can be solved to optimality while significantly decreasing the search time.     

紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.