Sobre la necesidad del desarrollo de algoritmos informáticos

Abstract

This article emerges as the summary of the end-of-degree project in the Mathematics degree by the same author under the tutelage of Professor Miguel Delgado² Pineda in the 2022-2023 academic year. The aim of this document is to reflect an algorithm developed in Python to enable the search for the minimum value of any continuous function in Rn with box constraints. Convex functions optimization can be supported by several properties that make the calculation and design of algorithms easier, which don’t apply for non-convex functions. This makes the search for the minimizers more difficult since obtaining a local minimum does not guarantee at all that it corresponds to the global minimum, as it does in the optimization of convex functions [11]. In this document, different increasingcomplexity examples will be considered to show the need for computer programs in their resolution. Later, together with its code, there will be considered an algorithm with that goal: the cubic algorithm [3]. Development in Python programming language has been proposed due to the ease it entails, both in reading its code as well as in the libraries that it implements with several mathematical tools.