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.

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