Forum on Developments and Origins of Operations Research

Speaker: Jane J. Ye

Jane J. Ye works as a professor of mathematics at University of Victoria. Her interests include nonsmooth optimization and variational analysis, with a strong focus on bilevel optimization and its applications. She was born in China and received her B.Sc from Xiamen University in 1982. She held a Killam postgraduate scholarship from 1987 to 1990 while completing a PhD at Dalhousie University under the supervision of Michael Dempster. From 1990 to 1992 she was a postdoctoral researcher at the Centre de Recherches Mathématiques in Montreal, under the supervision of Francis Clarke. She joined University of Victoria in 1992 with an NSERC Women's Faculty Award, and has been a full professor since 2002. Prof. Ye serves as an associate editor of SIAM J. Optim., Math. Oper. Res. and Set-Valued Var. Anal. She is also the recipient of 2015 Krieger-Nelson Prize, given annually by the Canadian Mathematical Society to an outstanding female researcher in mathematics.

Materials

Optimality conditions for the mathematical program with equilibrium constraints via variational analysis

Bilevel programming programs: introduction, reformulation and partial calmness

Bilevel programs: directional constraint qualifications and necessary optimality conditions

Difference of convex algorithms for bilevel programs with applications in hyperparameter selection

Recordings (in Bilibili)

https://space.bilibili.com/1254993141/ 

Topic: BILEVEL PROGRAM AND MATHEMATICAL PROGRAM WITH EQUILIBRIUM CONSTRAINTS VIA VARIATIONAL ANALYSIS

This course consists of four lectures devoted to using variational analysis as a tool to study bilevel programs and mathematical program with equilibrium constraints.

Optimality conditions for the mathematical program with equilibrium constraints via variational analysis

November 23, 2021, 10:00--11:30 UTC+8

In this lecture, I will explain why the mathematical program with equilibrium constraints is an intrinsic nonconvex and nonsmooth optimization problem even when all defining functions are smooth. I will then discuss how we could use the tool of variational analysis to derive various optimality conditions.

Bilevel programs: introduction, reformulations, and partial calmness condition

November 25, 2021, 10:00--11:30 UTC+8

In this lecture, I will first give an introduction to bilevel programs. Then I will discuss difficulties in studying bilevel programs and review various reformulations for bilevel programs. Finally, I will discuss the concept of partial calmness condition.

Bilevel programs: directional constraint qualifications and necessary optimality conditions

November 23, 2021, 10:00--11:30 UTC+8

This lecture is devoted to constraint qualifications and KKT conditions for bilevel programs. Directional optimality condition is sharper than the classical KKT condition while directional constraint qualification is weaker than the classical nondirectional one. I will explain how we could obtain verifiable directional constraint qualification and directional necessary optimality conditions for bilevel programs.

DC bilevel algorithms with applications in hyperparameter optimization

November 27, 2021, 10:00--11:30 UTC+8

In this lecture, I will first explain how one can use convex analysis as a tool to design algorithms for solving a class of nonsmooth bilevel program which is a class of bilevel programs where the upper level objective function is a difference of (nonsmooth) convex functions and the lower level programs are fully convex (but nonsmooth). Then I will discuss its applications in hyperparameter selection in machine learning.