My research focuses on the design, analysis, and implementation of algorithms for continuous and discrete nonlinear optimization, as well as their application to scientific and engineering problems.
My work on numerical algorithms for nonlinear optimization includes the following topics
- Interior-point methods for nonlinear nonconvex optimization
- Optimization methods for mathematical problems with complementarity constraints
- Optimization methods for machine learning problems
- Optimization methods for nonconvex continuous optimization with inexact step computation
- Branch-and-bound and outer-approximation-based method for mixed-integer nonlinear optimization
- Computational lithography
- Hyperthermia treatment planning
- Circuit tuning (optimization of transistor widths in digital circuits)
See the software section.