论文标题
用贝叶斯推理和拓扑优化的应用简化非凸优化的通缩
Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization
论文作者
论文摘要
非凸优化问题具有多个局部最佳解决方案。非凸优化问题通常在许多应用中发现。最近提出的一种方法是有效地探索多个局部最佳解决方案而没有随机重新定位的方法，取决于通缩概念。在本文中，讨论了在非凸优化和非线性系统求解中使用通缩的不同方法。提出了一种简单，一般和新颖的通缩约束，以便能够与现有的非线性编程求解器或非线性系统求解器一起使用通缩。提出了提议的通缩约束与最小距离约束之间的连接。此外，讨论了通缩约束的许多变化及其局限性。最后，提出了拟议方法论在近似贝叶斯推论和拓扑优化领域的许多应用。
Non-convex optimization problems have multiple local optimal solutions. Non-convex optimization problems are commonly found in numerous applications. One of the methods recently proposed to efficiently explore multiple local optimal solutions without random re-initialization relies on the concept of deflation. In this paper, different ways to use deflation in non-convex optimization and nonlinear system solving are discussed. A simple, general and novel deflation constraint is proposed to enable the use of deflation together with existing nonlinear programming solvers or nonlinear system solvers. The connection between the proposed deflation constraint and a minimum distance constraint is presented. Additionally, a number of variations of deflation constraints and their limitations are discussed. Finally, a number of applications of the proposed methodology in the fields of approximate Bayesian inference and topology optimization are presented.
