Based on an eigenvalue study, a descent class of Dai–Liao conjugate gradient methods is proposed. An interesting feature of the proposed class is its inclusion of the efficient nonlinear conjugate gradient methods proposed by Hager and Zhang, and Dai and Kou, as special cases. It is shown that the methods of the suggested class are globally convergent for uniformly convex objective functions. Numerical results are reported, they demonstrate the efficiency of the proposed methods in the sense of the performance profile introduced by Dolan and Moré.

Using unmanned aerial vehicles (UAVs) to cover users in wireless networks has increased in recent years. Deploying UAVs in appropriate positions is important to cover users and nodes properly. In this article, we propose an efficient approach to determine the minimum number of required UAVs and their optimal positions. To this end, we use an iterative algorithm that updates the number of required UAVs at each iteration. To determine the optimal position for the UAVs, we present a mathematical model and solve it accurately after linearizing. One of the inputs of the mathematical model is a set of candidate points for UAV deployments in 2-D space. The mathematical model selects a set of points among candidate points and determines the altitude of each UAV. To provide a suitable set of candidate points, we also propose a candidate point selection method: the MergeCells method. The simulation results show that the proposed approach performs better than the 3-D P-median approach introduced in the literature. We also compare different candidate point selection approaches, and we show that the MergeCells method outperforms other methods in terms of the number of UAVs, user data rates, and simulation time.

In the Internet of Things networks deploying fixed infrastructure is not always the best and most economical solution. Advances in efficiency and durability of Unmanned Aerial Vehicles (UAV) made flying small cell base stations (BS) a promising approach by providing coverage and capacity in environments where using fixed infrastructure is not economically justified. A key challenge in covering an area with UAV-based small cell BSs is optimal positioning the UAVs to maximize the coverage and minimize the number of required UAVs. In this paper, we propose an optimization problem that helps to determine the number and position of the UAVs. Moreover, to have efficient results in a reasonable time, we propose complementary heuristic methods that effectively reduce the search space. The simulation results show that our proposed method performs better than genetic algorithms.