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Algorithms for Large-Scale Nonlinearly Constrained Optimization

大规模非线性约束优化算法

基本信息

批准号：
EP/F005369/1
负责人：
Nicholas Ian Mark Gould
金额：
$ 42.85万
依托单位：
University of Oxford
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2007
资助国家：
英国
起止时间：
2007 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FF005369%2F1
关键词：
Algorithms Large Scale Nonlinearly Constrained

项目摘要

The solution of large-scale nonlinear optimization-- minimization ormaximization - problems lies at the heart of scientificcomputation. Structures take up positions of minimal constrainedpotential energy, investors aim to maximize profit while controllingrisk, public utilities run transmission networks to satisfy demand atleast cost, and pharmaceutical companies desire minimal drug doses totarget pathogens. All of these problems are large either because themathematical model involves many parameters or because they are actuallyfinite discretisations of some continuous problem for which thevariables are functions.The purpose of this grant application is to support the design, analysisand development of new algorithms for nonlinear optimization that areparticularly aimed at the large-scale case.We shall focus on methods which attempt to improve simplified (cheaper) approximations of the actual (complicated) problem.Such a procedure may be applied recursively, and the mostsuccessful ideas in this vein are known as sequential quadraticprogramming (SQP). Our research is directed on ways to improve onSQP particularly when the underlying problem is large, and indeedparticularly in the case where SQP itself may be too expensive tocontemplate. The end goal of our research is to produce high-quality, publicly available software as part of the GALAHAD library.

大规模非线性优化问题的解决方案--最小化或最大化--是科学计算的核心。结构占据了最小限制势能的位置，投资者的目标是在承担风险的同时实现利润最大化，公共事业运营传输网络以最低成本满足需求，制药公司希望最小的药物剂量来靶向病原体。所有这些问题都很大，要么是因为数学模型涉及许多参数，要么是因为它们实际上是某些变量为函数的连续问题的有限离散化。分析和发展非线性优化的新算法，特别是针对大规模的情况。我们将集中在试图改善简化（更便宜）的方法。实际（复杂）问题的近似。这样的过程可以递归地应用，这方面最成功的思想被称为序列二次规划（SQP）。我们的研究是针对如何改善SQP，特别是当潜在的问题很大时，尤其是在SQP本身可能太昂贵而无法考虑的情况下。我们研究的最终目标是生产高质量的，公开可用的软件作为GALAHAD库的一部分。