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In recent years, the multi-objective optimization (vector optimization) problems has been actively studied and widely applied in many fields of science such as medicine, economics, finance, engineering, radio resource management, discrete optimization, variational inequality, computational biology, machine design and control, environmental science, agriculture, production and management activities, etc.In this book we propose a nonmonotone methods to solve the multi-objective optimization problem, which makes use of approximation to Hessian matrices of the objective functions by diagonal positive matrices in computing search direction.Finally, we proved the effectiveness of the proposed methods by numerical experiments.