AF: Small: Approximate Augmented Lagrangians: First-Order and Parallel Optimization Methods, with Applications to Stochastic Programming

AF：小：近似增广拉格朗日：一阶和并行优化方法，及其在随机规划中的应用

• 批准号: 1115638
• 负责人: Jonathan Eckstein
• 金额: $ 35.85万
• 依托单位: Rutgers University Newark
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-15 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1115638&HistoricalAwards=false
• 关键词: AF; Small; Approximate; Augmented; Lagrangians

Continuous optimization is a mathematical discipline with extensiveapplications in engineering design and business/logistical planning.Its currently most common solution techniques are difficult to adaptto newly evolving computer architectures comprising dozens tothousands of processing elements working in parallel. Combiningseveral existing techniques with some recent results of the principalinvestigator, this project explores a means of solving continuousoptimization problems that should adapt more readily to parallelcomputer architectures than present standard solvers, allowing thearchitectures' full power to be brought to bear on large,time-consuming problems. Without such new solution approaches,solution of critical design and planning problems may not benefit frommost of the advances in computing power anticipated for the nextdecade. The project will also involve cooperative work with theBrazilian research community.The technical approach is to capitalize on recent advances inaugmented Lagrangian and conjugate gradient algorithms to produce anew kind of modular parallel continuous constrained optimizationsolver. The solver consists of a classical augmented Lagrangian outerloop, with subproblems solved by the a state-of-the artbox-constrained conjugate gradient method terminated by a recentlydeveloped relative error criterion. The research consists of threestages: the goal of stage one is to create an object-oriented, modularserial implementation, test it extensively, and address sometheoretical issues. Stage two aims to evolve the stage-one substrateinto a parallel solver for which the user explicitly specifies how tomap the problem structure to multiple processing elements. Stagethree's goal is to automate the structure detection and mappingprocess. Stages two and three will use stochastic programmingproblems as test cases.

连续优化是一门在工程设计和商业/物流规划中有着广泛应用的数学学科，其目前最常用的求解技术很难适应由数十到数千个并行处理单元组成的新的计算机体系结构。 结合几个现有的技术与最近的一些结果的principalinvestigator，该项目探讨了解决连续优化问题的方法，应该更容易适应并行计算机架构比目前的标准求解器，使架构的全部权力，以承担大型，耗时的问题。 如果没有这些新的解决方案，关键的设计和规划问题的解决方案可能不会受益于未来十年预计的计算能力的大部分进步。该项目还将涉及与巴西研究界的合作工作。技术方法是利用最新的进展开创拉格朗日和共轭梯度算法，以产生一种新的模块化并行连续约束优化求解器。 求解器包括一个经典的增广拉格朗日外环，与子问题解决的一个国家的最先进的框约束共轭梯度法终止最近开发的相对误差标准。 本研究分为三个阶段：第一阶段的目标是建立一个面向对象的，模块化的串行实现，广泛的测试，并解决一些理论问题。 第二阶段的目标是发展阶段一基板成一个并行求解器，用户明确指定如何映射的问题结构，以多个处理元素。 第三阶段的目标是自动化结构检测和映射过程。 第二阶段和第三阶段将使用随机规划问题作为测试用例。