Nonlinear Optimization

Abstract

Throughout this chapter, we only treat the minimization problem for convex functions (see Definition 24.23). Furthermore, in most cases, we assume that the objective function being minimized is a quadratic function. These minimization assumptions may easily cover the cases where a function needs to be maximized. In the case of concave functions (Definition 24.25), where we are interested in the maxima, the function may be multiplied by -1 which inverts it into a convex function such that the location of the maximum now points to the minimum of the new function. So, the maximization function is changed to a minimization function.