Optimization Algorithms and Simulation Based Optimization

Outline

Challenges for optimization

Simulation First, then Optimization

Fluid Control by MEMS Devices  (Tsai, Byrd,N)

"Current:"

Two Cases

State-of-the-art algorithms

"Exception LANCELOT:"

Satisfying the Constraints  (Newton Krylov)

First Difficulty: Failure of Newton-Krylov

Optimization

Part I: Full Space Approach

Full Space Approach: ideal case

Full Space Approach: iterative method

Pros/Cons

Part II: Null Space Approach

Null Space Approach
Iterative method on null space of constraints

"Advantages of null space approach"

"Challenges of null space approach"

Preconditioning

"One possible approach"

Null-Space Approach: Pros

Null-Space Approach: Cons

Part III: Unconstrained Formulation