约束Minimax问题的一个带积极集识别的简单序列二次约束二次规划算法.pdf

广西大学硕士学位论文约束Minimax问题的一个带积极集识别的简单序列二次约束二次规划算法姓名:邱丽娟申请学位级别:硕士专业:运寿学与控制论指导教师:简金宝 20110527 约束Minimax问题的一个带积极集识别的简单序列二次约束二次规划算法摘要本学位论文在光滑约束优化问题的简单序列二次约束二次规划算法和minimaX问题积极集识别技术基础上,提出了一个求解带非线性约束的 ,在每次迭代过程中,(避免Maratos效应),— nom而tz约束规格(MFcQ),数值试验表明,对于所测试的问题,. 第l章为绪论,除研究背景外,重点介绍和回顾与本文有关的可行方向法的思想和积极集识别技术,由此引出本文的主要思想. 第2章,给出本文的算法步骤和算法所具有的一些性质. 第3章,在弱MFcQ条件下证明算法具有全局收敛性. 第4章,在包含上层严格互补等较温和条件下证明算法具有强收敛性和超线性收敛性. 第5章,对算法进行一些初步的数值试验,以说明算法的有效性. 关键词:约束minimaX问题序列二次约束二次规划可行方向法积极集识别全局和超线性收敛性 ASIMPLE SEQUENTIAL QUADRAT工CALLy CONSTRAINED QUADRATIC PROGRAMMING ALGORITHM WITH ACTIVE IDENTIFICATION SETS FOR CONSTRAINED MINIMAX PROBLEMS ABSTRACT Inthisthesis,the nonlinear minimax problems with inequality con. straints are on theideasofsimple sequential quadrat— ically constrained quadratic programming algorithm forsmooth con— strained optimization and auctiveident泊cation sets forminimax Dro卜 lems,we propose analgorithm forsolVing thediscussed thepreVious work,at each iteration,afeaSible direction ofdescent called main direction isobtained bysolVing only one subprogram which is coHl_ posed of a conVex quadraticaUy objective mnction and simple quadratic inequality constraints without the8econd derivatives oftheconstrained correction direction(to avoid theMaratos e如ct)is yielded by s01ving asystem oflinearequations(SLE)which includes only thecons七raints and theirgradients corresponding tothe active identificationset,thus,the scaleandtheconputation cost ofthe high—order correction direction are deceased. The proposed algorithm possesses 910bal coIlvergence under weak Mangasarian—Flomovitz con. strainedqualification(MFCQ)and superlinear convergence under mild conditions with theupper—level l