Bregman Proximal Gradient Algorithm with Extrapolation for a class of Nonconvex Nonsmooth Minimization Problems

In this paper, we consider an accelerated method for solving nonconvex and nonsmooth minimization problems. We propose a Bregman Proximal Gradient algorithm with extrapolation(BPGe). This algorithm extends and accelerates the Bregman Proximal Gradient algorithm (BPG), which circumvents the restrictive global Lipschitz gradient continuity assumption needed in Proximal Gradient algorithms (PG). The BPGe algorithm has higher generality than the recently introduced Proximal Gradient algorithm with extrapolation(PGe), and besides, due to the extrapolation step, BPGe converges faster than BPG algorithm. Analyzing the convergence, we prove that any limit point of the sequence generated by BPGe is a stationary point of the problem by choosing parameters properly. Besides, assuming Kurdyka-{\'L}ojasiewicz property, we prove the whole sequences generated by BPGe converges to a stationary point. Finally, to illustrate the potential of the new method BPGe, we apply it to two important practical problems that arise in many fundamental applications (and that not satisfy global Lipschitz gradient continuity assumption): Poisson linear inverse problems and quadratic inverse problems. In the tests the accelerated BPGe algorithm shows faster convergence results, giving an interesting new algorithm.Comment: Preprint submitted for publication, February 14, 201

Benchmarking the Physical-world Adversarial Robustness of Vehicle Detection

Adversarial attacks in the physical world can harm the robustness of detection models. Evaluating the robustness of detection models in the physical world can be challenging due to the time-consuming and labor-intensive nature of many experiments. Thus, virtual simulation experiments can provide a solution to this challenge. However, there is no unified detection benchmark based on virtual simulation environment. To address this challenge, we proposed an instant-level data generation pipeline based on the CARLA simulator. Using this pipeline, we generated the DCI dataset and conducted extensive experiments on three detection models and three physical adversarial attacks. The dataset covers 7 continuous and 1 discrete scenes, with over 40 angles, 20 distances, and 20,000 positions. The results indicate that Yolo v6 had strongest resistance, with only a 6.59% average AP drop, and ASA was the most effective attack algorithm with a 14.51% average AP reduction, twice that of other algorithms. Static scenes had higher recognition AP, and results under different weather conditions were similar. Adversarial attack algorithm improvement may be approaching its 'limitation'.Comment: CVPR 2023 worksho

An Optimized, Easy-to-use, Open-source GPU Solver for Large-scale Inverse Homogenization Problems

We propose a high-performance GPU solver for inverse homogenization problems to design high-resolution 3D microstructures. Central to our solver is a favorable combination of data structures and algorithms, making full use of the parallel computation power of today's GPUs through a software-level design space exploration. This solver is demonstrated to optimize homogenized stiffness tensors, such as bulk modulus, shear modulus, and Poisson's ratio, under the constraint of bounded material volume. Practical high-resolution examples with 512^3(134.2 million) finite elements run in less than 32 seconds per iteration with a peak memory of 21 GB. Besides, our GPU implementation is equipped with an easy-to-use framework with less than 20 lines of code to support various objective functions defined by the homogenized stiffness tensors. Our open-source high-performance implementation is publicly accessible at https://github.com/lavenklau/homo3d