项目名称: 非光滑约束优化束方法和梯度取样法研究
项目编号: No.11301095
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 唐春明
作者单位: 广西大学
项目金额: 22万元
中文摘要: 非光滑优化是最优化研究的重要分支,不仅有重要的理论意义,而且广泛应用于最优控制、工程设计和图像处理等实际领域。本项目研究求解非光滑约束优化的束方法和梯度取样(GS)法。研究内容与创新主要有:(1)基于"上-下"多面体近似模型、DC分片仿射模型、二次逼近模型及bundle修正策略等,提出求解非光滑约束优化的新型束方法;(2)构建非光滑约束优化的强次可行GS方法、内点型GS方法、信赖域型GS方法和filter型GS方法,并利用无导数技术、梯度近似技术和自适应技术等,对提出方法进一步改进,旨在减少计算量、加快收敛速度;(3)探索将GS思想融入到束方法中,提出一类新型非光滑方法:GS-束方法;(4)针对minimax问题的特殊结构,结合增量型技术、无导数技术、聚集技术和多面体近似技术等,提出约束minimax问题的束方法和GS方法;(5)分析论证算法的收敛性,并进行大量数值试验,验证算法的有效性。
中文关键词: 非光滑优化;束方法;极大极小;割平面模型;全局收敛
英文摘要: Nonsmooth optimization is an important branch of optimization studies. It not only has important theoretical value, but also is widely used in practical problems, such as optimal control, engineering design and image processing, etc. This project studies the bundle methods and gradient sampling (GS) methods for solving nonsmooth constrained optimization. The research contents and innovation are: (1) to propose new bundle methods for solving nonsmooth constrained optimization based on upper-lower polyhedral approximation model, DC piecewise affine model, quadratic approximation model and bundle modification strategy, etc; (2) to design strongly sub-feasible GS method, interior point GS method, trust region GS method and filter GS method for nonsmooth constrained optimization, and to improve the proposed methods by the use of nonderivative technique, gradient approximation technique and adaptive technique, in order to reduce the computational cost and accelerate the rate of convergence; (3) to present a new class of nonsmooth method: GS-bundle method by incorporating GS idea into bundle methods; (4) aiming at the special structure of minimax problems, to propose new bundle methods and GS methods for solving constrained minimax problems by combining the incremental technique, nonderivative technique, aggregation t
英文关键词: Nonsmooth optimization;Bundle method;Minmimax;Cutting-planes model;Global convergence