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Title: Advancing the Velocity Gradient Technique: Using Gradient Amplitudes and Handling Thermal Broadening
Award ID(s):
1816234
PAR ID:
10191899
Author(s) / Creator(s):
;
Date Published:
Journal Name:
The Astrophysical Journal
Volume:
898
Issue:
1
ISSN:
1538-4357
Page Range / eLocation ID:
65
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. Gradient sampling (GS) methods for the minimization of objective functions that may be nonconvex and/or nonsmooth are proposed, analyzed, and tested. One of the most computationally expensive components of contemporary GS methods is the need to solve a convex quadratic subproblem in each iteration. By contrast, the methods proposed in this paper allow the use of inexact solutions of these subproblems, which, as proved in the paper, can be incorporated without the loss of theoretical convergence guarantees. Numerical experiments show that, by exploiting inexact subproblem solutions, one can consistently reduce the computational effort required by a GS method. Additionally, a strategy is proposed for aggregating gradient information after a subproblem is solved (potentially inexactly) as has been exploited in bundle methods for nonsmooth optimization. It is proved that the aggregation scheme can be introduced without the loss of theoretical convergence guarantees. Numerical experiments show that incorporating this gradient aggregation approach can also reduce the computational effort required by a GS method. 
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