Lagrangian Relaxation for Mixed-Integer Linear Programming: Importance, Challenges, Recent Advancements, and Opportunities

Operations in areas of importance to society are frequently modeled as Mixed-Integer Linear Programming (MILP) problems. While MILP problems suffer from combinatorial complexity, Lagrangian Relaxation has been a beacon of hope to resolve the associated difficulties through decomposition. Due to the non-smooth nature of Lagrangian dual functions, the coordination aspect of the method has posed serious challenges. This paper presents several significant historical milestones (beginning with Polyak's pioneering work in 1967) toward improving Lagrangian Relaxation coordination through improved optimization of non-smooth functionals. Finally, this paper presents the most recent developments in Lagrangian Relaxation for fast resolution of MILP problems. The paper also briefly discusses the opportunities that Lagrangian Relaxation can provide at this point in time

On the Influence of Corpuscular Fluxes and of Electron Photoloosening Reaction on the Formation of the D-Layer of the Ionosphere

Effect of corpuscular fluxes and electron photoloosening reaction on formation of ionospheric D laye

Quantitative Estimation of the Ratio of GABA-Immunoreactive Cells in Neocortical Grafts

Somatosensory anlage from 17-18 day old rat embryos were transplanted in place of the removed barrel cortex in adult rats. Six to eight months after transplantation, the grafts were either completely separated by glial scar or partly separated and partly confluent with the host neocortex. Each was studied histologically and immunostained for GABA. It was found that in partly confluent grafts the neuronal density was similar or even higher than in the host cortex, while the cell number in the separate grafts was much lower than in the nearby host cortex. The number of GABA-positive cells, however, was in all grafts significantly lower (2.9% on average) than in the normal cortex (11.8% on average).The decline in GABA-stained nerve cells was highest in separated grafts, but was somewhat less marked in transplants partly confluent with the host tissue. The possible role of partial or total deafferentation as well as the relative vulnerability of the transplanted tissue by temporary hypoxia and other metabolic disturbances are discussed as the probable factors in selective decline of GABA-ergic cells in the transplanted somatosensory cortex

TO THE ISSUE HARDENING OF DRILLING EQUIPMENT PARTS

This paper considers the possibility of optimal hardened layer of parts operating in conditions of high abrasive wear. The experiments on obtaining of parts with a hardened layer, conducted their research of the macro and micro structure of the resulting coating thickness and wear resistance.Южно-Уральский государственный университет выражает благодарность за финансовую поддержку Министерства образования и науки Российской Федерации (грант № 11.9658.2017/БЧ)

Inspecting aviation composites at the stage of airplane manufacturing by applying 'classical' active thermal NDT, ultrasonic thermography and laser vibrometry

The results of applying three nondestructive testing techniques to the inspection of parts of a new Russian TVS-2DTS airplane made of carbon fiber reinforced plastic are presented. A basic technique implemented in workshop conditions implements optical stimulation of inspected parts. The usefulness of ultrasonic infrared thermography combined with laser vibrometry in the evaluation of parts with complicated geometry is illustrated. Samples with artificial and real defects have been tested in workshop conditions

Surrogate Lagrangian Relaxation: A Path To Retrain-free Deep Neural Network Pruning

Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline significantly increases the overall training time. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation, which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem. We prove that our method ensures fast convergence of the model compression problem, and the convergence of the SLR is accelerated by using quadratic penalties. Model parameters obtained by SLR during the training phase are much closer to their optimal values as compared to those obtained by other state-of-the-art methods. We evaluate our method on image classification tasks using CIFAR-10 and ImageNet with state-of-the-art MLP-Mixer, Swin Transformer, and VGG-16, ResNet-18, ResNet-50 and ResNet-110, MobileNetV2. We also evaluate object detection and segmentation tasks on COCO, KITTI benchmark, and TuSimple lane detection dataset using a variety of models. Experimental results demonstrate that our SLR-based weight-pruning optimization approach achieves a higher compression rate than state-of-the-art methods under the same accuracy requirement and also can achieve higher accuracy under the same compression rate requirement. Under classification tasks, our SLR approach converges to the desired accuracy $3\times$ faster on both of the datasets. Under object detection and segmentation tasks, SLR also converges $2\times$ faster to the desired accuracy. Further, our SLR achieves high model accuracy even at the hard-pruning stage without retraining, which reduces the traditional three-stage pruning into a two-stage process. Given a limited budget of retraining epochs, our approach quickly recovers the model's accuracy.Comment: arXiv admin note: text overlap with arXiv:2012.1007