Nonlinear Optimization
Cetraro, July 1-7, 2007

Interior Point Methods

Prof. Tamas Terlaky, McMaster University, Hamilton, Ontario, Canada


Abstract


This course give concise introduction to the basic concepts, models and algorithmic paradigms of interior point methods for large classes of optimization problems.
Algorithmic issues and some novel modeling tools are discussed as well.

1) Interior Point Methods (IPMs) for Linear Optimization (LO)
a) Feasible IPMs
- existence and convergence of the central path
- primal-dual path following interior point methods, a complexity proof
- extension to convex quadratic optimization and complementarity problems
b) Initialization strategies
- the self-dual embedding model
- infeasible interior point methods
c) simplex versus interior point methods; pros and cons
2) IPMs for Conic Linear Optimization
- conic duality and the central path
- the second order conic optimization (SOCO) problem
- the semidefinite optimization (SDO) problem
- IPMs for SOCO and SDO
- robust optimization; robust LO and robust SOCO
- applications and the SeDuMi software package
3) IPMs for Nonlinear Optimization
- IPMs for smooth convex nonlinear optimization
- IPMs for general nonlinear optimization problems, also including
 complementarity conditions