Abstract Unmanned aerial vehicles (UAVs), widely used due to their low cost and versatility, pose security and privacy threats, which calls for their reliable recognition at low altitudes. However, strong ground clutter and multipath effects severely interfere with the weak radar echoes reflected off the micro‐UAVs, resulting in severe degradation of recognition reliability. Based on channel modelling and UAV recognisability analysis, a time‐frequency transform‐aided contrastive learning model is proposed to suppress the severe ground clutter and reliably recognise low‐altitude UAVs. In the proposed framework, a time‐frequency transform unit is first applied to suppress the multipath‐induced ambiguity effect and ease the semantic feature extraction via Zhao‐Atlas‐Marks transform and morphological operation. Thereafter, a contrastive‐learning‐based feature extraction and fusion unit is established to suppress non‐target clutter interference and extract recognisable semantic UAV features. Finally, a gated recurrent unit‐based classifier is designed for UAV recognition. Sufficient experiments are carried out on both real and simulated data sets, and the comparative results verify that the proposed model outperforms the mainstream algorithms and improves the detection accuracy by more than 5% under severe ground clutter interference.

The separable convex resource allocation problem with nested bound constraints aims to allocate B units of resources to n activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve this model exactly. Our algorithm is capable of solving instances with millions of activities in several minutes. The running time of our algorithm is at most 73% of the running time of the current best algorithm for benchmark instances with three classes of convex objectives. The efficiency of our algorithm derives from a combination of constraint relaxation and divide and conquer based on infeasibility information. In particular, nested bound constraints are relaxed first; if the solution obtained violates some bound constraints, we show that the problem can be divided into two subproblems of the same structure and smaller sizes according to the bound constraint with the largest violation. Summary of Contribution. The resource allocation problem is a collection of optimization models with a wide range of applications in production planning, logistics, portfolio management, telecommunications, statistical surveys, and machine learning. This paper studies the resource allocation model with prescribed lower and upper bounds on the total amount of resources consumed by nested subsets of activities. These nested bound constraints are motivated by storage limits, time-window requirements, and budget constraints in various applications. The model also appears as a subproblem in models for green logistics and machine learning, and it has to be solved repeatedly. The model belongs to the class of computationally challenging convex mixed-integer nonlinear programs. We develop a combinatorial algorithm to solve this model exactly. Our algorithm is faster than the algorithm that currently has the best theoretical complexity in the literature on an extensive set of test instances. The efficiency of our algorithm derives from the combination of an infeasibility-guided divide-and-conquer framework and a scaling-based greedy subroutine for resource allocation with submodular constraints. This paper also showcases the prevalent mismatch between the theoretical worst-case time complexity of an algorithm and its practical efficiency. We have offered some explanations of this mismatch through the perspectives of worst-case analysis, specially designed instances, and statistical metrics of numerical experiments. The implementation of our algorithm is available on an online repository.