非凸优化收缩的简化及其在贝叶斯推理和拓扑学中的应用optimization
Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization
摘要：
非凸优化问题具有多个局部最优解。非凸优化问题在许多应用中很常见。最近提出的方法之一，有效地探索多个局部最优解，而无需随机重新初始化依赖于收缩的概念。本文讨论了放气在非凸优化和非线性系统求解中的不同使用方法。提出了一种简单、通用和新颖的放气约束，使放气与现有的非线性规划求解器或非线性系统求解器一起使用。提出的放气约束和最小距离约束之间的连接。此外，通货紧缩的限制和他们的局限性的变化进行了讨论。最后，一些应用所提出的方法在近似贝叶斯推理和拓扑优化领域。
英文摘要：
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.
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