【摘要】 在不考虑设备故障的前提下,一个工作站的服务质量主要取决于其负荷大小。本文建立了工作站负荷最小的优化模型,设计了一种变量转换方法,并经适当的约束条件合并将该非线性的、具有不等式约束的模型转化为凸优化模型。推导给出该凸优化模型对应的拉格朗日函数及其最优解存在的KKT条件,并引入凸优化内点法作为负荷配置的有效计算工具。实例计算结果表明,凸优化内点算法具有迭代次数少、收敛速度快的优点;实际应用中可以将非线性的复杂优化问题凸性化,从而得到其最优解。更多还原

【Abstract】 The service quality of a workstation depends mainly on its service load. In this paper, an optimization model with inequality constraints is proposed, which aims to minimize the service load. A novel transformation of optimization variables is also devised and the constraints are properly combined so as to make this model into a convex one, whose corresponding Lagrange function and the KKT(Karush-Kuhn-Tucker) conditions are established afterwards. The interior-point method for convex optimization is presented here as an efficient computation tool. Finally, this model is evaluated by a real example, from which conclusions are reached that the interior-point method possesses advantages such as faster convergence and fewer iterations and it is possible to make complicated nonlinear optimization problems exhibit convexity so as to obtain the optimum.更多还原