Theory and methodology for nonlinear optimization

  • Semidefinite programming and conic programming
  • Integer programming
  • Primal-dual methods for large-scale convex optimization
  • Self-concordant convex optimization
  • Numerical methods for nonlinear optimization such as sequential convex programming and Gauss-Newton methods.
  • Optimality and constant rank constraint qualification in optimization.

Variational inequalities and equilibrium problems

  • Optimization under uncertainty; stochastic optimization and equilibria
  • Sensitivity analysis for variational inequalities and equilibrium problems
  • confidence regions and intervals for stochastic variational inequalities.
  • Sensitivity analysis of traffic user equilibria
  • Inference for sparse penalized statistical regression

Applications of Optimization

  • Optimal control, linear and nonlinear model predictive control (MPC)
  • Linear feedback controller design
  • Machine learning and statistics
  • Image and signal processing, and compressive sensing
  • Operations Research