Title
Strong Duality in Risk-Constrained Nonconvex Functional Programming
Abstract
In this talk, we will discuss a novel result establishing that a wide class of nonconvex risk-constrained functional optimization problems exhibits strong duality, regardless of nonconvexity.
We consider risk constraints featuring convex and positively homogeneous risk measures admitting dual representations with bounded risk envelopes, generalizing expectations. Popular risk measures supported within our setting include the conditional value-at-risk (CVaR), the mean-absolute deviation (MAD, including the non-monotone case), certain distributionally robust representations and more generally all real-valued coherent risk measures on the space L1. Our core proof technique appears to be new and relies on risk conjugate duality in tandem with J. J. Uhl’s weak extension of A. A. Lyapunov’s convexity theorem for vector measures taking values in general infinite-dimensional Banach spaces.
We highlight the usefulness of our result by discussing specific applications in resource allocation for wireless communication systems and supervised constrained machine learning.
Bio
Spyridon Pougkakiotis is a Lecturer in Optimisation in the Department of Mathematics, King’s College London. His research focuses on several aspects of continuous optimisation and its applications in operational research, engineering and data science. Spyridon received a BSc in Informatics and Telecommunications from the University of Athens (2016). Afterwards, he received an MSc in Operational Research with Computational Optimisation from the School of Mathematics of the University of Edinburgh (2017), where he stayed and completed his PhD in Optimisation (2022), for which he received the 2022 OR Society Doctoral Award. He then joined the Electrical Engineering Department of Yale University as a postdoctoral research associate (2022-2023), before joining the University of Dundee as a Lecturer in Mathematics (2023-2024).