Introduction to Optimization
Undergraduate course, Ecole des Ponts, 1A, 2026
This is a 3rd year course giving a first introduction to optimization. It assumes basic linear algebra, multivariable calculus and real analysis, and goes from modeling and optimality conditions to increasingly structured problem classes.
The course follows the narrative modeling - mathematical guarantees - algorithms - numerical verification, and is organized in five parts:
- introduction: vocabulary, modeling, solvers and a word on complexity
- optimization under constraints: tangent cones, constraint qualifications, KKT and duality
- convex optimization: convex sets and functions, global optimality, gradient methods
- linear optimization: polyhedra, standard forms, simplex and LP duality
- mixed-integer linear programming: formulations, relaxations and branch and bound
Documents
- Course textbook (English) - contains the exercises and their solutions