# Simplifying deflation for non-convex optimization with applications in Bayesian inference and topology optimization

arXiv: https://arxiv.org/abs/2201.11926 · HTML: https://mlsanity.com/paper/2201.11926/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 40 references that are in the map.
- First posted on arXiv 28 Jan 2022.

## Builds on (most cited first, 9 of 9)

- [Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization](https://mlsanity.com/paper/1603.06560/) (2016)
- [BOHB: Robust and Efficient Hyperparameter Optimization at Scale](https://mlsanity.com/paper/1807.01774/) (2018)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Pathfinder: Parallel quasi-Newton variational inference](https://mlsanity.com/paper/2108.03782/) (2021)
- [Automatic Variational Inference in Stan](https://mlsanity.com/paper/1506.03431/) (2015)
- [Computing multiple solutions of topology optimization problems](https://mlsanity.com/paper/2004.11797/) (2020)
- [Tightening McCormick Relaxations for Nonlinear Programs via Dynamic Multivariate Partitioning](https://mlsanity.com/paper/1606.05806/) (2016)
- [An Adaptive, Multivariate Partitioning Algorithm for Global Optimization of Nonconvex Programs](https://mlsanity.com/paper/1707.02514/) (2017)
- [Deflation for semismooth equations](https://mlsanity.com/paper/1904.13299/) (2019)

## Built on by (most cited first, 1 of 1)

- [Diverse Rare Sample Generation with Pretrained GANs](https://mlsanity.com/paper/2412.19543/) (2024)

## Abstract (arXiv)

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.