The aim of the course is to recall some notions of linear algebra, introduce some basic concepts of calculus for several variables and develop the most important topics on unconstrained and constrained optimization.
Linear algebra: matrix algebra, determinants, rank, quadratic forms, sign of a quadratic form and definite matrices.
Calculus: functions of several variables, level sets, differential calculus for functions of several variables, convex functions.
Unconstrained optimization: first order optimality conditions, second order optimality conditions.
Constrained Optimization: the Weierstrass Theorem. Constrained optimization with equality constraints, Lagrange theorem. Lagrangian function and optimality conditions. Constrained optimization with inequality constraints, Kuhn-Tucker theorem. Convex problems.
Written exam. Intermediate tests are proposed during the course.
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