Research at FAST

80 Department of Applied Mathematics Department of Applied Mathematics Qualification BSc (LZU) MSc (DUT) PhD (UVic) ORCID ID 0000-0002-9135-9080 Dr BAI Kuang Research Assistant Professor Research Overview Dr Kuang Bai’s research area is comprised of optimization and variational analysis, as well as their applications in Economics, Engineering and Statistics. His main research specializations can be categorized under the following headers: • Bilevel programs with non-convex lower level programs • Mathematical programs with equilibrium constraints • Non-smooth and non-convex optimization problems • Stability and sensitivity for optimization problems • Existence of error bounds In particular, with collaborators, he has derived the directional versions of many classical constraint qualifications for a mathematical program under very general settings, which can include a large class of optimization problems. These constraint qualifications can recover their classical counterparts and can serve as sufficient conditions for necessary optimality conditions, existence of error bounds and can guarantee useful calculus rules for generalized subgradients. The results are theoretical and general, hence, can be applied to many optimization problems, like the convergence analysis of first-order algorithms. Meanwhile, he also studied the directional optimality conditions for bilevel programs. It is known that bilevel programs are popular in economics and management science, which however, are also very hard to study. Applying the recently developed directional variational analysis techniques, Dr Bai and his collaborators studied the sensitivity analysis of value functions and used the value function approach to develop very sharp optimality conditions for bilevel programs. His recent interests include studying constraint qualifications and optimality conditions for two-level stochastic programs and bilevel programs, as well as sufficient conditions for the existence of error bounds for structured mathematical programs. Representative Publication • Kuang Bai , Jane Ye and Jin Zhang. Directional quasi-/ pseudo-normality as sufficient conditions for metric subregularity, SIAM Journal on Optimization, 29( 2019 ), 2625-2649