• KSII Transactions on Internet and Information Systems (TIIS)
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• v.18 no.1
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• pp.211-232
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• 2024

In this paper, we consider the resource allocation and offloading decisions of device-to-device (D2D) cooperative UAV-assisted mobile edge computing (MEC) system, where the device with task request is served by unmanned aerial vehicle (UAV) equipped with MEC server and D2D device with idle resources. On the one hand, to ensure the fairness of time-delay sensitive devices, when UAV computing resources are relatively sufficient, an optimization model is established to minimize the maximum delay of device computing tasks. The original non-convex objective problem is decomposed into two subproblems, and the suboptimal solution of the optimization problem is obtained by alternate iteration of two subproblems. On the other hand, when the device only needs to complete the task within a tolerable delay, we consider the offloading priorities of task to minimize UAV computing resources. Then we build the model of joint offloading decision and power allocation optimization. Through theoretical analysis based on KKT conditions, we elicit the relationship between the amount of computing task data and the optimal resource allocation. The simulation results show that the D2D cooperation scheme proposed in this paper is effective in reducing the completion delay of computing tasks and saving UAV computing resources.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.1
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• pp.47-58
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• 2018

The heterogeneous cellular network (HCN) is most significant as a key technology for future fifth generation (5G) wireless networks. The heterogeneous network considered consists of randomly macrocell base stations (MBSs) overlaid with femtocell base stations (BSs). The stochastic geometry has been shown to be a very powerful tool to model, analyze, and design networks with random topologies such as wireless ad hoc, sensor networks, and multi- tier cellular networks. The HCNs can be energy-efficiently designed by deploying various BSs belonging to different networks, which has drawn significant attention to one of the technologies for future 5G wireless networks. In this paper, we propose switching off/on systems enabling the BSs in the cellular networks to efficiently consume the power by introducing active/sleep modes, which is able to reduce the interference and power consumption in the MBSs and FBSs on an individual basis as well as improve the energy efficiency of the cellular networks. We formulate the minimization of the power onsumption for the MBSs and FBSs as well as an optimization problem to maximize the energy efficiency subject to throughput outage constraints, which can be solved the Karush Kuhn Tucker (KKT) conditions according to the femto tier BS density. We also formulate and compare the coverage probability and the energy efficiency in HCNs scenarios with and without coordinated multi-point (CoMP) to avoid coverage holes.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.7
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• pp.3134-3155
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• 2020

In this paper, we study the joint radio and computational resource allocation in the ultra-dense mobile-edge computing networks. In which, the scenario which including both computation offloading and communication service is discussed. That is, some mobile users ask for computation offloading, while the others ask for communication with the minimum communication rate requirements. We formulate the problem as a joint channel assignment, power control and computational resource allocation to minimize the offloading cost of computing offloading, with the precondition that the transmission rate of communication nodes are satisfied. Since the formulated problem is a mixed-integer nonlinear programming (MINLP), which is NP-hard. By leveraging the particular mathematical structure of the problem, i.e., the computational resource allocation variable is independent with other variables in the objective function and constraints, and then the original problem is decomposed into a computational resource allocation subproblem and a joint channel assignment and power allocation subproblem. Since the former is a convex programming, the KKT (Karush-Kuhn-Tucker) conditions can be used to find the closed optimal solution. For the latter, which is still NP-hard, is further decomposed into two subproblems, i.e., the power allocation and the channel assignment, to optimize alternatively. Finally, two heuristic algorithms are proposed, i.e., the Co-channel Equal Power allocation algorithm (CEP) and the Enhanced CEP (ECEP) algorithm to obtain the suboptimal solutions. Numerical results are presented at last to verify the performance of the proposed algorithms.

• Journal of Electrical Engineering and Technology
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• v.13 no.3
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• pp.1069-1078
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• 2018

Demand response (DR) programs give opportunity to consumers to manage their electricity bills. Besides, distribution system operator (DSO) is interested in using DR programs to obtain technical and economic benefits for distribution network. Since small consumers have difficulties to individually take part in the electricity market, an entity named demand response provider (DRP) has been recently defined to aggregate the DR of small consumers. However, implementing DR programs face challenges to fairly allocate benefits and payments between DRP and DSO. This paper presents a procedure for modeling the interaction between DRP and DSO based on a bilevel programming model. Both DSO and DRP behave from their own viewpoint with different objective functions. On the one hand, DRP bids the potential of DR programs, which are load shifting and load curtailment, to maximize its expected profit and on the other hand, DSO purchases electric power from either the electricity market or DRP to supply its consumers by minimizing its overall cost. In the proposed bilevel programming approach, the upper level problem represents the DRP decisions, while the lower level problem represents the DSO behavior. The obtained bilevel programming problem (BPP) is converted into a single level optimizing problem using its Karush-Kuhn-Tucker (KKT) optimality conditions. Furthermore, point estimate method (PEM) is employed to model the uncertainties of the power demands and the electricity market prices. The efficiency of the presented model is verified through the case studies and analysis of the obtained results.