Research Initiation: An Extension of Local Monotonicity to Optimal Design of Large Systems of Mechanical Components

工程设计中的优化是设计过程中的一个重要方面。它的目的是更有效和合理地分配资源，从而提高生产率。本研究旨在将局部单调性推广到机械设计中经常遇到的机械大系统的优化设计中。利用分解理论的思想，将一个大规模的非线性约束设计优化问题分解为一组小问题。然后，这些小问题将被优化，并以规定的方式协调它们的解决方案，从而导致原始问题的解决。机械系统的设计和/或应用中出现的问题将作为指导性例子。这项工作的结果将补充现有的数值优化技术，特别是那些用于求解大规模约束非线性优化问题的技术。

Optimization in engineering design is an important aspect of the design process. It aims at a more efficient and rational allocation of resources resulting in improved productivity. This research aims at extension of local monotonicity to optimal design of large systems of mechanical components which are encountered very often in mechanical design. The idea of decomposition theory will be used to break down a large-scale nonlinearly constrained design optimization problem into a collection of small problems. These small problems will then be optimized and their solutions coordinated in a prescribed manner, leading to the solution to the original problem. Problems arising from the design and/or application of mechanical systems will be used as guiding examples. The result of this work will complement the existing numerical optimization techniques, in particular those which are used for solving large-scale constrained nonlinear optimization problems.