正定二次规划的一个对偶算法

给出了一个正定二次规划的对偶算法．算法把原问题分解为一系列子问题,在保持原问题的Wolfe对偶可行的前提下,通过迭代计算,由这一系列子问题的最优解向原问题的最优解逼近．同时给出了算法的有限收敛性．     

Modeling and Solving an Airline Schedule Generation Problem

Since opening a new flight connection or closing an existing flight has a great impact on the revenues of an airline, the generation of the flight schedule is one of the fundamental problems in airline planning processes.In this paper we concentrate on a special case of the problem which arises at charter companies. In contrast to airlines operating on regular schedules, the market for charter airlines is well-known and the schedule is allowed to change completely from period to period. Thus, precise adjustments to the demands of the market have a great potential for minimizing operating costs.We present a capacitated network design model and propose a combined branch-and-cut approach to solve this airline schedule generation problem. To tighten the linear relaxation bound, we add cutting planes which adjust the number of aircraft and the spill of passengers to the demand on each itinerary.For real-world problems from a large European charter airline we obtain solutions within a very few percent of optimality with running times in the order of minutes on a customary personal computer for most of the data sets.     

A Study of the Dennis-Wolkowicz Method on Convex Functions

In this paper, we analyze the global convergence of the least-change secant method proposed by Dennis and Wolkowicz, when applied to convex objective functions. One of the most distinguished features of this method is that the Dennis-Wolkowicz update doesn't necessarily belong to the Broyden convex family and can be close to the DFP update, but it still has the self-correcting property. We prove that, for convex objective functions, this method with the commonly used Wolfe line search is globally convergent. We also provide some numerical results.     

修正PRP共轭梯度方法求解无约束最优化问题

基于著名的PRP共轭梯度方法,利用CG_DESCENT共轭梯度方法的结构,本文提出了一种求解大规模无约束最优化问题的修正PRP共轭梯度方法。该方法在每一步迭代中均能够产生一个充分下降的搜索方向,且独立于任何线搜索条件。在标准Wolfe线搜索条件下,证明了修正PRP共轭梯度方法的全局收敛性和线性收敛速度。数值结果展示了修正PRP方法对给定的测试问题是非常有效的。     

一种改进的共轭梯度法及全局收敛性

本文在DY共轭梯度法的基础上对解决无约束最优化问题提出一种改进的共轭梯度法.该方法在Wolfe线搜索下能够保证充分下降性,并在目标函数可微的条件下,证明了算法的全局收敛性.大量数值试验表明,该方法是很有效的.