



01194nas a2200121   4500008004100000245004200041210004200083260001400125520083200139100001400971700001800985856006901003       2019                        eng d00aNew stepsizes for the gradient method0 aNew stepsizes for the gradient method  c1/28/20193 a<p>Gradient methods are famous for their simplicity and low complexity, which attract more and more attention for large scale optimization problems. A good stepsize plays an important role to construct an efficient gradient method. This paper proposes a new framework to generate stepsizes for gradient methods applied to convex quadratic function minimization problems. By adopting different criterions, we propose four new gradient methods. For 2-dimensional unconstrained problems with convex quadratic objective functions, we prove that the new methods either terminate in finite iterations or converge R-superlinearly; for n-dimensional problems, we prove that all the new methods converge R-linearly. Numerical experiments show that the new methods enjoy lower complexity and outperform the existing gradient methods.</p>1 aSun, Cong1 aLiu, Jin-Peng  uhttps://quics.umd.edu/publications/new-stepsizes-gradient-method