Jane Ye

My broad research interests include optimization and optimal control theory and algorithms.

In my recent research, I apply variational analysis to the following four very important problems arising from Economics, Engineering, Operations Research and Management Science. (1) The bilevel program 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. (2) The principal-agent problem is a fundamental problem that frequently occurs in Economics, Management Science and Political Science. It treats the difficulties that arise under conditions of incomplete and asymmetric information when a principal hires an agent to pursue the principal's interests but the agent's action is unobservable. (3) The Stackelberg differential game model is a bilevel optimization problem where both levels are optimal control problems. In recent years, it has been used to model applications in Management Science such as supply chain management and marketing channels, specifically conflicts and coordination issues. (4) In Science, Social Sciences and Engineering, regression models have been playing a major role and the least squares estimator has been widely used. Optimal design of experiments is defined as finding designs such that one can get accurate information about the regression model or the regression parameter from its least squares estimator. These problems are all intrinsically nondifferentiable and nonconvex and hence very difficult to solve. Variational analysis is an extension of convex analysis to encompass a variety of nondifferentiable functions (convex or nonconvex) and mappings. Variational analysis provides a powerful tool to study the problems I propose to solve. The goal of my research is to develop theories and algorithms for solving these problems.

Interests

• Optimization
• optimal controls
• variational analysis
• bilevel programming
• optimal design of experiments

Courses

• Fall 2023: MATH 301: Complex Variables  MATH 347: Introduction to Continuous Optimization 
• Spring 2024:
• Summer 2024:

Selected Publications

• M. Xu, J. J. Ye and L. Zhang, Smoothing SQP methods for solving degenerate nonsmooth constrained optimization problems with applications to bilevel programs, SIAM Journal on Optimization, vol. 25, 1388-1410, 2015.
• L. Guo, G. Lin, J. J. Ye and J. Zhang, Sensitivity Analysis of the value function for parametric mathematical programs with equilibrium constraints SIAM Journal on Optimization, vol. 24, 1206-1237, 2014.
• C. Ding, D. Sun and J. J. Ye, First order optimality conditions for mathematical programs with semidefinite cone complementarity constraints, Mathematical Programming, series A, vol. 147, 539-579, 2014.
• G. Lin, M. Xu and J. J. Ye, On solving simple bilevel programs with a nonconvex lower level program, Mathematical Programming, series A, vol. 144, 277-305, 2014.
• J. J. Ye and J. Zhang, Enhanced Karush-Kuhn-Tucker condition and weaker constraint qualifications, Mathematical Programming, series B, vol. 139, 353-381, Issue 1, 2013.
• L. Guo, J. J. Ye and J. Zhang, Mathematical programs with geometric constraints in Banach spaces: enhanced optimality, exact penalty, and sensitivity, SIAM Journal on Optimization, vol. 23, Issue 4, 2295-2319, 2013.
• J.J. Ye and J. Zhou, Minimizing the condition number to construct design points for polynomial regression models, SIAM Journal on Optimization, vol. 23, issue 1, 666-686, 2013.
• L. Guo, G. Lin and J. J. Ye, Stability analysis for parametric mathematical programs with geometric constraints and its applications, SIAM Journal on Optimization, vol. 22, issue 3, 1151-1176, 2012.
• J. J. Ye and D. Zhu, New necessary optimality conditions for bilevel programs by combining MPEC and the Value Function Approach, SIAM Journal on Optimization, vol. 20, issue 4, 1885-1905, 2010.
• H. Xu and J. J. Ye , Necessary optimality conditions for two-stage stochastic programs with equilibrium constraints, SIAM Journal on Optimization, vol. 20, issue 4, 1685-1715, 2010.