同伦内点法求一类多目标优化问题的最小弱有效解

本文针对客观实际中不同决策者在已有条件下自我需求实现问题,根据"自报公议"原则,将多目标优化问题转化成含有权系数变量的一个新单目标优化问题.利用组合同伦内点法来求解单目标问题,通过路径跟踪得到多目标优化问题的最小弱有效解,从而实现"公议",达到相对最佳目的,并证明了该方法是整体收敛的.     

Interior-point methods for symmetric optimization based on a class of non-coercive kernel functions

In this paper, we generalize polynomial-time primal–dual interior-point methods for symmetric optimization based on a class of kernel functions, which is not coercive. The corresponding barrier functions have a finite value at the boundary of the feasible region. They are not exponentially convex and also not strongly convex like many usual barrier functions. Moreover, we analyse the accuracy of the algorithm for this class of functions and we obtain an upper bound for the accuracy which depends on a parameter of the class.     

基于有限障碍的全牛顿步内点算法

针对线性规划问题,文中引入了一种与传统障碍函数不同的新的障碍函数,其在可行域边界上的取值是有限的.沿此有限障碍函数所确定的新的搜索方向,给出了短步长全牛顿步内点算法,结果证明该算法具有目前求解线性规划问题最好的复杂性界.     

考虑发电约束的输电断面最大传输能力

为了打破以往输电能力求解过程中发电机端电压维持不变的假设,提出了考虑发电约束求解最大输电能力(TTC)的新方法.根据大型风电场并网及同步发电机调速器和励磁系统等动态元件的运行限制,建立了计算输电断面最大输电能力的优化模型,并采用信赖域内点法进行序列迭代求解.在信赖域内,将非线性优化问题逼近为线性规划(LP)子问题,以构造的价值函数为依据调整信赖域半径.在New England 39节点算例系统中验证了模型和计算方法的有效性.实验结果表明,考虑发电约束的输电断面最大传输能力计算结果更接近系统的实际运行情况.     

面向对象的无功优化软件开发与应用

介绍一套完全采用面向对象的概念及编程技术开发的电网无功优化计算软件。该软件充分利用了Visual C 在可视化程序实现方面的优势，将电力系统的各种元件用对象表示，并以数据为中心开发通用的数据交换接口，使程序具有很好的通用生和可扩展性，该软件及其采用的线性规划内点法具有良好的实用性和适用性，已应用于广东电网的无功优化，取得了满意的优化效果。     

Control applications of nonlinear convex programming

Since 1984 there has been a concentrated effort to develop efficient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their efficiency for LP): they extend gracefully to nonlinear convex optimization problems. New interior-point algorithms for problem classes such as semidefinite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme efficiency of modern linear programming codes. In this paper we discuss three examples of areas of control where our ability to efficiently solve nonlinear convex optimization problems opens up new applications. In the first example we show how SOCP can be used to solve robust open-loop optimal control problems. In the second example, we show how SOCP can be used to simultaneously design the set-point and feedback gains for a controller, and compare this method with the more standard approach. Our final application concerns analysis and synthesis via linear matrix inequalities and SDP.     

国际数学规划领域的热点问题：线性规划内点法

论述20世纪80年代至今的国际数学规划领域的热点问题——线性规划内点法的出现和它的理论体系、研究现状及其发展，同时也讨论了传统的单纯形法的最新进展以及内点法与单纯形法的对比测试，展现了该领域当前的研究现状与发展趋势。     

Interior point gradient algorithm for totally nonnegative least-squares problems in inequality sense

In this paper we study a scaled interior-point gradient algorithm for totally nonnegative least-squares problems in the inequality sense. The global convergence of the algorithm is established. Finally, extensive computational comparison with the so-called generalized Newton algorithm is given showing the superior performance of the gradient-based algorithm.     

An interior-point sequential approximate optimization methodology

The use of optimization in a simulation-based design environment has become a common trend in industry today. Computer simulation tools are commonplace in many engineering disciplines, providing the designers with tools to evaluate a designs performance without building a physical prototype. This has triggered the development of optimization techniques suitable for dealing with such simulations. One of these approaches is known as sequential approximate optimization. In sequential approximate minimization a sequence of optimizations are performed over local response surface approximations of the system. This paper details the development of an interior-point approach for trust-region-managed sequential approximate optimization. The interior-point approach will ensure that approximate feasibility is maintained throughout the optimization process. This facilitates the delivery of a usable design at each iteration when subject to reduced design cycle time constraints. In order to deal with infeasible starting points, homotopy methods are used to relax constraints and push designs toward feasibility. Results of application studies are presented, illustrating the applicability of the proposed algorithm.