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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. 

Reliable environmental context prediction is critical for wearable robots (e.g., prostheses and exoskeletons) to assist terrain-adaptive locomotion. This article proposed a novel vision-based context prediction framework for lower limb prostheses to simultaneously predict human's environmental context for multiple forecast windows. By leveraging the Bayesian neural networks (BNNs), our framework can quantify the uncertainty caused by different factors (e.g., observation noise, and insufficient or biased training) and produce a calibrated predicted probability for online decision-making. We compared two wearable camera locations (a pair of glasses and a lower limb device), independently and conjointly. We utilized the calibrated predicted probability for online decision-making and fusion. We demonstrated how to interpret deep neural networks with uncertainty measures and how to improve the algorithms based on the uncertainty analysis. The inference time of our framework on a portable embedded system was less than 80 ms/frame. The results in this study may lead to novel context recognition strategies in reliable decision-making, efficient sensor fusion, and improved intelligent system design in various applications.