Qualifier
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An oral presentation I gave for my PhD qualifier examination
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Qualifier
- 1. Qualifier Exam in HPC February 10 th , 2010
- 2. Quasi-Newton methods Alexandru Cioaca
Editor's Notes
- Ball and beam, Navier-Stokes, stability of an airplane wrt to pilot commands. nonlinear systems, number of variables = number of equations The solution means determining some values of variables/parameters that strictly satisfy the given relationships (equations). Impossible to solve them by hand even if they are homogeneous.
- Direct solve – reuse the factorization (quasi-implicit Newton, chord method)
- Computational fluid dynamics – millions of variables (chesapeake bay)
- Examples of cost functions Talk about differentiability
- Convergence rates - LINEAR We want Bk to mimic the behavior of newton => symmetric positive definite (at least in a neighborhood)
- Trust regions determine a region around the current iterate where the approximate model of the objective function is accurate. The step is taken to be the minimizer on the trust region.
- Explain symmetry, positive definiteness Limited memory quasi-newton
- Z_k can be taken to be the