Global optimization using homotopy with 2-step predictor-corrector method

Abstract

In this research, we suggest a new method for solving global optimization problem by improving Homotopy Optimization with Perturbations and Ensembles (HOPE) method. Our new method, named as Homotopy 2-Step Predictor-corrector Method (HSPM) is based on the intermediate Value Theorem (IVT) coupled with modified Predictor-Corrector Halley method (PCH) for solving global optimization problem. HSPM does not require a good initial guess since it contains the element of homotopy, which is a globally convergent method. This paper discusses the time complexity of the new algorithm, which makes it more efficient than HOPE.

Algorithm for Solution of Non-convex Optimization Problem Through Piece-wise Convex Transformation

“…Another attempt done by modified HOPE is called Homotopy with 2-Step Predictor-corrector Method (HSPM) in 2014. HSPM can be considered as the precursor of I-HSPM, please refer [13] for details. From the simulation of [14], we noticed the influence of a small value of λ is not strong which causes HSPM to have a lot of unnecessary function evaluations.…”

Homotopy optimisation based NMF for audio source separation

“…In [36], NMF was used to separate sources using maximum a posteriori estimation and Itakura-Saito divergence. In [43][44][45][46][47][48][49][50][51], homotopy-based methods have been used for solving nonconvex problems arising in many different applications. Continuous methods provide a very strong alternative for other global optimisation solutions as they reduce computation time and given the right selection of homotopy function and parameters that guarantee the global convergence of the solution.…”