Doctoral Award Winner Presentation
Talk Title: A Regularised Interior Point Method for Convex Programming
Solving complex mathematical problems efficiently is crucial in various fields. Interior Point Methods (IPMs) are commonly used techniques known for providing accurate solutions relatively quickly. However, they face challenges such as dealing with inaccurate numbers and tricky mathematical scenarios.
To overcome these challenges, researchers have explored modified versions of IPMs that demonstrate improved stability in real-world situations. Despite the success of these modifications in practical applications, a comprehensive theoretical understanding has been lacking until recently.
This presentation introduces a combination of an infeasible IPM and the Proximal Method of Multipliers (PMM), forming a method referred to as IP-PMM. This combined approach acts as a more reliable version of IPMs, specifically suited for certain types of mathematical problems. The method involves applying a few rounds of the interior point method to smaller mathematical sub-problems within the Proximal Method of Multipliers. Once a satisfactory solution is found for the sub-problem, adjustments are made, a new set of problems is formulated, and the process is repeated.
A significant aspect of the work is demonstrating that this method is not excessively time-consuming for a broad range of problems, marking a notable advancement in mathematical research. By leveraging the speed of IPMs and the stability of PMMs, the IP-PMM approach shows promise as an efficient solution.
To broaden the applicability of our approach, general strategies for efficiently solving associated mathematical problems within the IP-PMM framework will be discussed. Additionally, numerical results across various mathematical problems, highlighting the advantages of the modifications in IPMs and confirming the reliability and efficiency of the proposed IP-PMM algorithm.