| Course Description : | Mathematical optimization problem formulation, main general classifications of optimization problems, convexity, theory of constrained optimization, relevant geometric concepts (tangent and normal cones, theorems of the alternative, and separation results), constraint qualifications, geometric and algebraic expression of first-order optimality conditions, second-order optimality conditions, duality, some general important classes of nonlinear convex optimization problems (such as quadratic programming, second-order cone programming, and semidefinite programming (formulation and examples)), augmented Lagrangian methods, elements of interior-point methods. |