This course is intended to review some concepts of linear algebra and 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.
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