1. Linear optimization - Formulation of linear optimization models: decision variables, objective and constraints. - Applications to the optimization of business decisions. - Graphical solution and optimality of vertex solutions. - Duality, optimality test and sensitivity analysis: interpretation and applications. - Software-based numerical solution. 2. Integer optimization - Formulation of integer optimization models. - Applications to the optimization of business decisions. - Linear relaxations. Bounding the optimality gap of a feasible solution. Optimality test. - The Branch & Bound method and software-based numerical solution. 3. Unconstrained nonlinear optimization - Formulation of unconstrained nonlinear optimization models. - Applications to the optimization of business decisions. - Local and global optimality conditions. - Software-based numerical solution. 4. Equality-constrained nonlinear optimization - Formulation of equality-constrained nonlinear optimization models. - Applications to the optimization of business decisions. - Local and global optimality conditions via Lagrange multipliers. - Software-based numerical solution. 5. Inequality-constrained nonlinear optimization - Formulation of inequality-constrained nonlinear optimization models. - Applications to the optimization of business decisions. - Local and global optimality conditions via Karush-Kuhn-Tucker multipliers. - Software-based numerical solution.