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Implementation of new algorithm for steepest descent method
(Maltepe Üniversitesi, 2009) Mamat, Mustafa bin; Yee, Aw Siew; Mohd, Ismail bin
Exact line searches along each steepest descent direction converge very slowly. Barzilai and Borwein suggested two stepsizes that ensures superlinear convergence and performs quite well. Barzilai-Borwein method is not monotone, thus it is not easy to be generalized for general nonlinear functions. A new stepsize enables fast convergence and possesses monotone property is proposed by Yuan. The new stepsize is modifled to obtain modifled new steepest descent method, which is for convex quadratic problems only is proposed by Yuan. The new steepest descent method uses the new stepsize after every m exact line search iterations. An algorithm for m=2 is proposed in this paper. We use quadratic functions to test the performance of our algorithm.