Optimisation is a key tool in modelling. The aim of this course is to present the field of optimisation to students through its essential processes for formalising the problem posed and its useful techniques for econometrics, statistics, microeconomics and macroeconomics.
- Geometry for optimisation– Polarity and Farkas’ lemma, cones, the case of a set of constraints.
- Optimisation in $R^n$– Conditions for an open set, conditions for any set, conditions for a convex set, applications.
- Convex optimisation under constraints– Kuhn-Tucker conditions, solving the Lagrange problem, Kuhn-Tucker multipliers, applications.
- Example optimisation problems– Parametered optimisation, linear optimisation, quadratic optimisation and applications.
- Numerical methods for solving optimisation problems– Optimisation without constraints, optimisation with constraints (penalisation, dual methods).
- Dynamic programming– Introduction, discrete-time optimality principle, Hamilton-Jacobi-Bellman equation.
– Convex Optimization, S. Boyd and L. Vandenberghe, Cambridge University Press.
– Lectures on Modern Convex Optimization, A. Nemirovski and A. Ben-Tal, SIAM.