Global Optimization in Social System Engineering

在过去的两年中，我们开发了有效的算法计算全局最优解的一些低秩非凸极小化问题的特殊结构。其中较重要的结果如下：（1）发展了一个求多胞形上几个线性分式函数之和与乘积极小化的有效算法。(2)提出了一种求解凹二次规划问题全局极小点的有效启发式算法。(3)利用一种新的分枝定界算法，提出了求解均值-方差-偏度模型的一种有效算法。(4)针对一类带反凸约束的极小化问题，提出了一种分块/割平面算法。(5)开发了一种有效的启发式算法，用于解决与汽轮机优化运行相关的非凸极小化问题。(6)完成了题为“低秩非凸结构优化”的专著（Kluwer Academic Publishers，1996），这是我们过去十年在全局优化方面所做努力的集合。

In the last two years, we developed efficient algorithms for calculating globally optimal solutions of a number of low rank nonconvex minimization problems by exploiting their special structures. Among the more important results are the following :(1) Developed an efficeint algorithm for minimizing the sum and the product of several linear fractional functions over a polytope.(2) Developed an efficient heuristic algorithm for obtaining a global minimum point of concave quadratic programming problems.(3) Proposed an efficient algorithm for solving a mean-variance-skewness model by applying a new branch-and-bound algorithm.(4) Proposed a partitioning/cutting plane algorithm for a class of minimization problems with a set of reverse convex constraints.(5) Developed an efficient heuristic algorithm for solving a nonconvex minimization problem associated with an optimal operation of steam turbines.(6) Completed a monograph entitled "Optimization on Low Rank Nonconvex Structures" (Kluwer Academic Publishers, 1996), a collection of our efforts in global optimization during the past decade.