Research Highlights

Sensitivity Analysis in Nonlinear Semidefinite Programming: I have been conducting research on sensitivity analysis in nonlinear semidefinite programming (SDP) for over 25 years. My journey began in 1999 with Professor Jie Sun, when we established the strong semismoothness of the metric projector over the SDP cone. By taking advantage of this property, I solved the long-standing open question of characterizing the strong regularity of nonlinear SDP problems. The next milestone is the characterization of the robust isolated calmness for a class of conic programming problems. This line of inquiry culminated in achieving a long-standing goal: demonstrating that the Aubin property is equivalent to Robinson’s strong regularity at a local optimal solution for nonlinear SDP. What follows is a brief overview of my research in this area.

Augmented Lagrangian Methods for Solving Composite Conic Peogramming:

Smoothing Newton Methods with Global and Local Superlinear Convergence:

Symmetric Gauss-Seidel Iterations and Halpern Peaceman-Rachford Acceleration Methods:

Extragradient Methods for Monotone Variational Inequalities under Continuity:

More to come shortly…