To address the problem that the limited field of view of single camera of widely deployed highway surveillance cameras makes it difficult to achieve large-scale continuous perception， a cross-camera Bird’s-Eye View （BEV） road geometric alignment task was proposed to improve scene consistency and completeness. However， this task faces challenges due to the perspective differences and structural misalignments among multi-camera images. The horizon， as a global geometric prior， can unify these perspective differences， but its detection is easily affected by occlusion and environments， limiting alignment accuracy. To solve this problem， a horizon detection method for cross-camera BEV road alignment， named RoadHoriNet （Road Horizon detection Network）， was proposed. Firstly， perspective transformation and bounding box cropping were applied for data augmentation. Secondly， a diamond space representation was introduced to alleviate instability in vanishing-point learning. Thirdly， Receptive-Field Attention Convolution （RFAConv） and upsampling by Dynamic Sampling （DySample） were used to enhance feature representation and reconstruction accuracy. Finally， a geometric consistency loss function was designed to enhance the constraints of the orientation and position of horizon detection. Experimental results demonstrate that on the BrnoCompSpeed dataset， RoadHoriNet achieves a pixel error of 5.166%， an angle error of 0.032 5°， and a detection accuracy of 94.834%， while reducing the pixel error by 4.815 percentage points and the angle error by 0.019 4° compared with the adaptive horizon detection method. In the task of cross-camera BEV road geometry alignment， the relative alignment accuracy of RoadHoriNet reaches at least 99.129% after being corrected by the RoadHoriNet method， demonstrating its practicality and generalization potential in real-world traffic environments. It can be seen that RoadHoriNet provides a stable geometric prior for camera pose normalization and multi-camera coordinate unification， improving the relative alignment accuracy and robustness of cross-camera BEV road geometric alignment significantly.

To address the problem that the existing intelligent recommendation do not consider decision cost constraints， an intelligent recommendation model incorporating decision cost constraints and a Lagrangian solution algorithm were proposed. Firstly， based on the user-item rating matrix， the SVD++ （Singular Value Decomposition Plus Plus） model was adopted to predict unknown ratings of users on items. Secondly， according to the predicted ratings， a single-objective optimization model of intelligent recommendation under decision cost and distribution diversity constraints was constructed. Thirdly， the distribution diversity constraint was relaxed into the objective function， and a Lagrangian relaxation model under decision cost constraint was established. Finally， a dual sub-gradient algorithm based on greedy strategy was designed to solve the constructed Lagrangian relaxation model efficiently. Experimental results on the MovieLens dataset show that compared with the Gurobi solver， the proposed algorithm reduces the solution time by at least 90.317% significantly， with the objective function value decreased by no more than 0.694%； compared with the LightGCN （Light Graph Convolution Network） method， the constructed model achieves higher recommendation accuracy on all test cases， and improves the distribution diversity on 77.8% of cases. The above fully verifies the comprehensive advantages of the proposed model and solution algorithm in terms of efficiency and performance.