Andrea Ghezzi

University of Freiburg

Tuesday, October 15, 2024, 11:00 - 12:15

SR 01-012

The talk focuses on mixed-integer (nonlinear) optimization and covers mostly formulation techniques. We will present the basic notions to understand the branch-and-bound algorithm.

Online participation via Zoom link:

https://uni-freiburg.zoom-x.de/j/62791737415?pwd=UDJnbkZlS3NkVm1TSVZLSWxHSktZZz09 

Agenda: 

• Through examples we analyze the concepts of strength and size of a MIP formulation
  • What is a sharp formulation? and locally ideal?
  • Should we always aim for sharp formulations?
• What is MIP representable?
• Projected formulations (big-M method)
  • Common modeling techniques:
    • lookout and indicator variables
    • disjunctive constraints
    • boolean operators via binary modeling
    • alternatives to bilinear terms
    • modelling nonconvex piecewise-linear functions
• Extensions to mixed-integer nonlinear programming (MINLP) modeling
  • Best practice to prevent undesired behaviors
• Focus on models for mixed-integer optimal control problems (MIOCPs)
  • Formulations for mixed-integer conic problems (MICPs)
    • Piecewise linear dynamical systems:
      • MLD models
    • Automatic formulation techniques:
      • Graphs of convex sets
  • Formulation for MINLPs:
    • Nonlinear dynamical systems with binary inputs
    • MIOCP with logical conditions (aka "state-triggering constraints")