Optimization Comprehensive Exam
Information for Doctoral students taking a comprehensive examination in Optimization Theory.
Topics
- Review of optimization in R^n
- Classical problems of the calculus of variations
- Convex optimization
- Optimal control theory
- Proof of the Pontryagin maximum principle
- Applications
- Special topics (controllability, bang-bang principle).
Bibliography:
- E.R. Pinch, Optimal control and the calculus of variations
- B. Dacorogna, Introduction to the calculus of variations
- L.C. Evans, An introduction to mathematical optimal control theory
- V. Barbu, Optimal control of variational inequalities
- D. Motreanu and N.H. Pavel, Tangency, flow Invariance for differential equations and optimization problems
