Unconstrained optimisation via linear dimensionality reduction method

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BASIL NAIF OLAYAN ALHARBI
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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.
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