- Convexity. Properties of convex and strongly convex functions.
- First and second order optimality conditions. Lagrange multipliers and duality.
- Gradient method.
- Line searches.
- Newton and quasi-Newton methods.
- Subgradient method.
- Conjugate gradient.
- Usawa method.
- Cutting plane and bundle methods.
- Dynamic and dual dynamic programming with cut selection.
- Implementation of numerical optimization algorithms.
- Risk measures.
- Chance-constrained problems.
- Robust Stochastic Approximation.
- Stochastic Mirror Descent.
- Multi-cut decomposition methods with cut selection.
- M. Bandarra and V. Guigues. Multicut decomposition methods with cut selection for multistage stochastic programs. Optimization OnLine, 2017.
- J.F. Bonnans, J.C. Gilbert, C. Lemarechal, and C. Sagastiz ́ abal. ́ Numerical optimization: theoretical and practical aspects. Springer, 2003.
- V. Guigues. Multistep stochastic mirror descent for risk-averse convex stochastic programs based on extended polyhedral risk measures. Mathematical programming, 163:169–212, 2016.
- A. Shapiro, D. Dentcheva, and A. Ruszczynski. ́ Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia, 2009.