Unconstrained optimisation via linear dimensionality reduction method
Abstract
An investigation was carried to create an algorithm for solving nonlinear optimisation problems.
Chemical engineers face large, complicated datasets, hence, the ability to represent and visualise such data is
of great importance in creating accurate models to make predictions. Dimensionality reduction helps us to
cross that bridge. Inspired by many research in the eld [1] [2] [3], an algorithm combining a popular linear
dimensionality reduction (PLS) along with trust regions is outlined to assess the applicability on nonlinear
optimisation problems. Functions for benchmarking optimisation solvers were used as seeds to create higher
dimensional functions with a low eective dimensionality. The results show a promising potential for the
algorithm, solving nonlinear optimisation problems regardless of the dimension size; although Goldstein-Price
function did not follow observed trend. Optimisation solvers typically require more function evaluations for
high dimensionality functions, an idea is introduced in the algorithm to solve these functions, with higher
accuracy solutions at lower function evaluations. The practicality of the algorithm was tested against a chemical
engineering case study. The goal for this research to spark a new approach to solving nonlinear optimisation
via linear dimensionality reduction techniques, inspiring further research in this area.