Journal of Convex Analysis 27 (2020), No. 2, 557--564
Copyright Heldermann Verlag 2020
Asymptotic Behavior of Continuous Descent Methods with a Convex Objective Function
Simeon Reich
Dept. of Mathematics, The Technion -- Israel Inst. of Technology, 32000 Haifa, Israel
sreich@technion.ac.il
Alexander J. Zaslavski
Dept. of Mathematics, The Technion -- Israel Inst. of Technology, 32000 Haifa, Israel
ajzasl@technion.ac.il
Given a Lipschitz and convex objective function on a Banach space, we revisit the class of regular vector fields introduced in our previous work on descent methods. We consider continuous descent methods for minimizing our objective function and establish two convergence results for those methods which are generated by regular vector fields. These results improve upon a convergence result which we obtained in our previous work.
Keywords: Banach space, complete metric space, convex function, descent method, regular vector field.
MSC: 37L99, 47J35, 49M37, 90C25, 90C30.
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