Unconstrained Function Optimization

This chapter presents the necessary and sufficient conditions for an optimum point in a scalar function. The same is then extended to vector functions. The determination of the optimum point in a quadratic function is presented next. This chapter does not consider constraints. A scalar function \(f(x)\in \mathbb {R}\) is shown in Fig. 2.1, where the minimum point is indicated as \(x^*\) given by the following expression.