Abstract

A bilevel programming problem is a sequence of two optimization problems where the constraint region of the upper level problem is determined implicitly by the solution set to the lower level problem. It can be used to model a two-level hierarchical system where the two decision makers have different objectives and make their decisions on different levels of hierarchy. Recently more and more applications including those in machine learning have been modelled as bilevel optimization problems. In this work, we present a Moreau envelope function based approach for solving a nontrivial class of bilevel programs and study its theoretical and numerical properties. In particular, this nontrivial class of bilevel programs provides a powerful modelling framework for dealing with applications arising from hyperparameter selection in machine learning. We demonstrate the performance of our algorithm to some classes of hyperparameter selection problems such as the RBF kernel support vector machine.

Bioography

Jane Ye is a Professor of Mathematics at the University of Victoria, Canada, specializing in nonsmooth optimization, variational analysis, and bilevel optimization. She earned her BSc from Xiamen University (1982) and her MBA (1986) and PhD (1990) from Dalhousie University. Joining the University of Victoria in 1992, she was promoted to Associate Professor in 1997 and Full Professor in 2002. Awarded the 2015 CMS Krieger–Nelson Prize, Dr. Ye has published over 100 papers and book chapters. She has served on the editorial boards of leading journals such as SIAM Journal on Optimization, Mathematics of Operations Research, and Set-Valued and Variational Analysis. In 2024 and 2025, she was ranked among the top 0.05% of researchers worldwide in mathematical optimization.