- 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. On-Line Optimization, 2017.
• J.F. Bonnans, J.C. Gilbert, C. Lemarechal and C. Sagastiz ́ abal. `Numerical optimization: theoretical and practical aspects. Springer, 2003.
• V. Guigues. Descent of stochastic mirror in several stages for convex risk-averse stochastic programs based on extended measures of polyhedral risk. Mathematical programming, 163: 169-212, 2016.
• Shapiro, D. Dentcheva and A. Ruszczynski. `` Lectures on Stochastic Programming: Modeling and Theory. SIAM, Philadelphia, 2009.