STTR Phase II: Integrated Software and Systems for Large-Scale Nonlinear Optimization

这个小型企业创新研究计划第二阶段的研究项目将解决集成非线性优化软件的设计和创建，该软件结合了非线性优化的互补方法，以在广泛的应用需求中实现强大的性能。本文主要研究光滑非线性约束优化问题，该问题作为混合整数非线性规划和全局优化中的子问题，直接出现在许多应用中。这项工作将采用数学收敛分析和对实际问题的广泛测试。研究结果将非线性优化软件提升到一个新的水平，基于自适应和通用的算法集合，而不是当前优化软件包采用的单一算法方法。非线性优化模型出现在不同的科学领域，如医学成像、海洋学、晶体学和气候建模，以及几乎所有的工程领域，半导体制造商的芯片特征放置，电力和天然气公用事业的能源管理。非线性优化也迅速成为财务和收入管理等领域决策分析的关键工具。通过使优化包更灵活、更可靠，这项研究将为当前的非线性优化应用提供更强大的支持，同时使新的、更雄心勃勃的应用成为可能。

This Small Business Innovation Research Program Phase II research project will address the design and creation of integrated nonlinear optimization software that combines complementary approaches to nonlinear optimization to achieve robust performance over a wide range of application requirements. The work will concentrate on the area of smooth nonlinearly constrained optimization, which arises directly in numerous applications and as a sub-problem in mixed-integer nonlinear programming and global optimization. The work will employ both mathematical convergence analyses and extensive testing on problems of practical interest. Results of the research will take nonlinear optimization software to a new level, based on an adaptive and versatile collection of algorithms in contrast to the single-algorithm approaches employed by current optimization packages.Nonlinear optimization models arise in diverse areas of science such as medical imaging, oceanography, crystallography, and climate modeling, and in almost all areas of engineering, chip feature placement for semiconductor manufacturers to energy management for electric and gas utilities. Nonlinear optimization is also rapidly becoming a key tool in decision analysis in such areas as finance and revenue management. By enabling optimization packages to be more fexible and more reliable, this research will lead to stronger support for current nonlinear optimization applications while making new, more ambitious applications possible.