数学优化模型中分枝定界法的研究

一些NP完全问题已有了在实际应用时值得一试的求解算法．本文通过对分枝定界法的进一步分析，采用这种算法，开展数学建模中最优化问题案例的研究．在求解“指派问题”等NP问题上提出分枝定界法的改良思路．     

Existence of Neighboring Feasible Trajectories: Applications to Dynamic Programming for State-Constrained Optimal Control Problems

In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi equation. This is achieved under a constraint qualification (CQ) concerning the interaction of the state and dynamic constraints. The novelty of the results reported here is partly the nature of (CQ) and partly the proof techniques employed, which are based on new estimates of the distance of the set of state trajectories satisfying a state constraint from a given trajectory which violates the constraint.     

一般形式线性规划最优解集的确定

导出一般形式线规划最优解集的结构，并使用有效的算法给出确定最优解集的计算步骤。     

Bifurcations in parametric nonlinear programming

Bifurcation and continuation techniques are introduced as a class of methods for investigating the parametric nonlinear programming problem. Motivated by the Fritz John first-order necessary conditions, the parametric programming problem is first reformulated as a closed system of nonlinear equations which contains all Karush-Kuhn-Tucker and Fritz John points, both feasible and infeasible solutions, and relative minima, maxima, and saddle points. Since changes in the structure of the solution set and critical point type can occur only at singularities, necessary and sufficient conditions for the existence of a singularity are developed in terms of the loss of a complementarity condition, the linear dependence constraint qualification, and the singularity of the Hessian of the Lagrangian on a tangent space. After a brief introduction to elementary bifurcation theory, some simple singularities in this parametric problem are analyzed for both branching and persistence of local minima. Finally, a brief introduction to numerical continuation and bifurcation procedures is given to indicate how these facts can be used in a numerical investigation of the problem.This research was supported by the Air force Office of Scientific Research through grant number AFOSR-88-0059.     

Worst Traffic Passing Virtual Frame Regulation: Analysis with Dynamic Programming

This paper studies a discrete-time queueing system in which the traffic regulation places an upper bound on the number of arrivals in each of the non-overlapping time windows (virtual frames) of a fixed length. The worst traffic passing through this traffic regulation is characterized. As a criterion for traffic comparison, this paper employs the weighted sum of queueing delays with the weighting factors decaying geometrically over the time horizon. This paper uses dynamic programming techniques and convexity argument to characterize the worst traffic.     

On approximation of dual spaces and dual operators

We study the connection between equations which approximate an initial abstract linear equation and the adjoint one. We prove that the operator which is adjoint to the approximating one approximates the adjoint operator. As examples we consider adjoint linear integral equations and mutually dual linear programming problems.     

可持续增长曲线模型及其参数估计的非线性规划方法

建立了两个能拟合，预测可持续增长过程的曲线模型，讨论了曲线模型的若干性质，给出了模型参数估计的非线性规划方法，通过两个实例的验证说明了模型拟合效果好，预测精度高。     

孔扩散阻力对多孔催化剂失活动力学的影响(英文)

目前,在强扩散区城中,失活催化反应的分离型动力学方程式仅能用于1级反应和1级独立失活系统。本文把此类方程式扩展应用于各种1,2级反应和1,2级独立失活系统,同时针对气-固相反应器中气相流动呈活塞流或全混流的情况,讨论了如何由实验求取有关的动力学速率常数值。研究结果表明,过程存在孔扩散阻力时,反应转化率随着反应时间降低的速率比无孔扩散阻力的情况要慢。此外,对浓度独立失活和分离型动力学方程的特征也作了论述。     

A note on adapting methods for continuous global optimization to the discrete case

In this note we show that various branch and bound methods for solving continuous global optimization problems can be readily adapted to the discrete case. As an illustration, we present an algorithm for minimizing a concave function over the integers contained in a compact polyhedron. Computational experience with this algorithm is reported.