Modified BFGS Method For Non-Convex Functions In Unconstrained Optimization

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Khawari, Fatemeh | 2023

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 56673 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahdavi Amiri, Nezameddin
Abstract:
Nonlinear optimization is concerned with finding optimal solutions of optimization problems, where the objective function or some constraints are nonlinear. Since many issues in science and engineering can be expressed and formulated as a nonlinear problem, we investigate BFGS method, a successful iterative quasi-Newton method, for solving non-convex problems in unconstrained optimization. The method is based on the work of Yuan and his colleagues, making use of modified weak Wolfe-Powell line search, introducing a certain condition, introducing the next point if the condition is met, introducing a parabolic function if the condition is not established and obtaining the projection point and not using the projection point in the BFGS update, to ensure global convergence. We implement the method and test the program on various test problems.
Keywords:
Projection Method ; Newton-Like Method ; Modified Weak Wolfe-Powel Line Search ; Modified BFGS Method ; Nonlinear Optimization

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