Scalar Optimization (or How to Make the Best Decision)

This chapter provides an intuitive introduction to the numerical methods of optimization, in particular to the elimination, the ellipsoid, the simplex, and the interior methods for optimization problems involving linear functions, the Newton and the steepest descent methods for the minimization of nonlinear functions without constraints, and the penalty methods for optimization problems with nonlinear constraints. The chapter contains applications to resource allocation of resources and shadow pricing (e.g., for the electricity market), recruitment policies and management of pandemics.