Optimization

Deterministic optimization:

  • 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.

Stochastic optimization:

  • Risk measures.
  • Chance-constrained problems.
  • Robust Stochastic Approximation.
  • Stochastic Mirror Descent.
  • Multi-cut decomposition methods with cut selection.

Basic Information

Workload
60 hours

Mandatory:

  • 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.

Complementary:

  • Ben-Tal e Nemirovski (2001) Lectures on Modern Convex Optimization, SIAM, Philadelphia.
  • Shapiro, Dentcheva e Ruszczynski (2009) Lectures on Stochastic Programming: Modeling and Theory, SIAM, Philadelphia.
  • Boyd e Vandenberghe (2009) Convex Optimization, Cambridge University Press.
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