Journal of Operational Research and Its Applications ( Applied Mathematics ) - Lahijan Azad University

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The search for finding the local minimization in unconstrained optimization problems and a fixed point of the gradient system of ordinary differential equations are two close problems. Limited-memory algorithms are widely used to solve large-scale problems, while Rang Kuta's methods are also used to solve numerical differential equations. In this paper, using the concept of sub-space method and fixed-step length and integration of line-search and trust-region techniques, an ODE-based hybrid method is proposed for solving large-scale optimization problems. Since the line-search methods may require more iteration for convergence, while Trust-region methods also require a lot of iteration to solve the constrained sub problem, a new class of methods is proposed in this way, which combines the best features of trust-region and line-search methods. The main feature of the proposed method is that the linear equation system is solved only once in order to obtain the experimental step.

Keywords: Unconstrained optimization, Ordinary differential equations, Limited memory methods, Line-search, Trust-region

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