Effective Algorithms for Structured Nonconvex Optimization Based on First- and Second-Order Methods and Convex Relaxations

该项目关注的是非凸优化问题的有效算法的开发和实现，具有特定的底层结构（例如，紧集上的二次规划，由机器学习应用引起的优化问题）。该项目旨在利用一阶和二阶信息，结合各种凸松弛和凸包络，试图获得越来越紧的最优值的上界和下界。提出的方法将在基准实例上实现和测试。

This project is concerned with the development and implementation of effective algorithms for nonconvex optimization problems with a particular underlying structure (e.g., quadratic programs on compact sets, optimization problems arising from machine learning applications). The project is aimed at utilising first-order and second-order information together with various convex relaxations and convex envelopes in an attempt to obtain increasingly tighter upper and lower bounds on the optimal value. The proposed methods will be implemented and tested on benchmark instances.