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

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.