Faculty of Mathematics, Yazd University, Yazd, Iran
Abstract
Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. Under appropriate conditions, we show that the proposed method is globally convergent without needing convexity assumption on the objective function. Comparative results show computational efficiency of the proposed method in the sense of the Dolan-More performance profiles.
Dehghani, R., Hosseini, M. M., & Bidabadi, N. (2019). The modified BFGS method with new secant relation for unconstrained optimization problems. Computational Methods for Differential Equations, 7(1), 28-41.
MLA
Razieh Dehghani; Mohammad Mehdi Hosseini; Narges Bidabadi. "The modified BFGS method with new secant relation for unconstrained optimization problems". Computational Methods for Differential Equations, 7, 1, 2019, 28-41.
HARVARD
Dehghani, R., Hosseini, M. M., Bidabadi, N. (2019). 'The modified BFGS method with new secant relation for unconstrained optimization problems', Computational Methods for Differential Equations, 7(1), pp. 28-41.
VANCOUVER
Dehghani, R., Hosseini, M. M., Bidabadi, N. The modified BFGS method with new secant relation for unconstrained optimization problems. Computational Methods for Differential Equations, 2019; 7(1): 28-41.
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