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Title: Gradient Sampling Methods with Inexact Subproblem Solutions and Gradient Aggregation
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.  more » « less
Award ID(s):
1740796
PAR ID:
10443242
Author(s) / Creator(s):
;
Date Published:
Journal Name:
INFORMS Journal on Optimization
Volume:
4
Issue:
4
ISSN:
2575-1484
Page Range / eLocation ID:
426 to 445
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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