文档介绍：GLoBAL oPTIMAL SoLUTIoN ALGORITHM FOR SoME NoNC oNVEX oPTIMIZATIoN PRoBLEMS A Dissertation Submitted to the Graduate School ofHenan Normal University inPartial Fulfillment oftheRequirements for the Degree ofMaster ofScience By Bai xtaodi Supervisor: Peiping April,2010 摘要全局最优化问题是一门研究非线性函数在某个区域上全局最优点的特征和计算方法的科学,广泛见于金融、网络和交通、化学工程、,使得传统的非线性规划技术很难用来求解,因此研究此类问题的求解算法既有重要意义,,其理论和算法也得到了很大发展,,针对几类特殊的全局优化问题,: 第一章,概括介绍了目前国内外几种主要的求解全局优化问题的确定性方法和随机性方法,以及它们的研究现状,并对本文所做的工作给予简单介绍. 第二章,针对一类非凸规划问题(NP),将由Jiao提出的全局优化方法与一个合适的删除技巧相结合,,,数值结果表明:通过采用这一新的删除技巧,在迭代次数,需要的链表长度和总的运行时间上,计算效率都有明显改进. 第三章,针对带离散约束的广义几何规划问题,,首先利用问题的特殊结构,构造了一个等价的带有离散约束的单调优化问题,,减小和调整操作能割掉最优解不存在的一大部分区域,,证明了所提方法能够保证收敛到全局最优解,并用数值试验表明了算法的可行性和有效性. 关键词:全局优化,非凸规划,单调优化,离散广义几何规划 II ABSTRACT The rescarch ofglobaloptimization methods focuses on the characteristic and corn— putional method oftheglobaloptimal point ofthenonlinear function over some convex or nonconvex optimizationproblems around work and transporta- tion,chemical engineering,molecular biology,environmental engineering,and tomulti—extremum property ofglobaloptimizationproblems,all theseproblems can not besolved easily byclassical nonlinear programming techniques,therefore,studing solu- tionsforthiskindofproblems not noly hasimportant significance,but alsohaschallenge development have been obtained inthetheorical andalgorithmaspects ofglobaloptimization due toimportant praticalapplications,but thereusually existsome problems during the course propose anew effectivemethod based on known theory and algorithms forsome special global optimal contents are as follows. InChapter 1,we introduce briefly severalmainly deterministicapproaches andstochas- wegi