Convex Optimization Method Research Articles

Unified Description and Optimization Method of Dual Active Bridge DC–DC Converters

The optimization of dual active bridge converters (DAB) is widely studied and numerous modulation schemes are proposed to enhance the performance of a DAB converter. However, a unified description method both suitable for time and frequency domain analysis still lacks. Besides, the optimization process encounters a difficulty of the potential nonconvex feasible region restricted by the power transmission equality, making the regular convex optimization methods no longer applicable. To solve these problems, this article gave a unified description method both suitable for time and frequency domain analysis based on the standard decomposition of instantaneous electric quantities. Besides, a unified optimization method is proposed based on tangent point searching for the feasible region and optimization objective surfaces. With the proposed unified optimization method, the optimization objective can be designed arbitrarily as long as it is piecewise continuous, and smooth. An efficiency-oriented optimization objective design method is introduced considering all electric quantities as well as the soft-switching conditions. Finally, the experimental results confirm the unified optimization method and the efficiency-oriented optimization objective design method.

Comparative Methods for Solving Optimal Power Flow in Distribution Networks Considering Distributed Generators: Metaheuristics vs. Convex Optimization

Objective: This article presents an analysis of different optimization methodologies, which aims to make an objective comparison between metaheuristic and convex optimization methods in distribution networks, focusing on the inclusion of distributed generation (DG). The MATLAB software is used as a tool for implementation and obtaining results. The objective was to determine the optimal size of the DGs to be integrated into the networks, with the purpose of reducing the active power losses (objective function). Methodology: Based on the specialized literature, the methodologies are selected, and the bases and conditions for the implementation of the optimization techniques are determined. In the case of second-order cone programming (SOCP), the relaxation of the nonlinear optimal power flow (OPF) problem is performed in order to use convex optimization. Then, the structures of each technique are established and applied in the MATLAB software. Due to the iterative nature of metaheuristic methods, the data corresponding to 100 compilations for each algorithm are collected. Finally, by means of a statistical analysis, the optimal solutions for the objective function in each methodology are determined, and, with these results, the different methods applied to the networks are compared. Results: By analyzing 33- and 69-node systems, it is demonstrated that metaheuristic methods are able to effectively size DGs in distribution systems and yield good results that are similar and comparable to SOCP regarding the OPF problem. Genetic algorithms (GA) showed the best results for the studied implementation, even surpassing the SOCP. Conclusions: Metaheuristic methods proved to be algorithms with a high computational efficiency and are suitable for real-time applications if implemented in distribution systems with well-defined conditions. These techniques provide innovative ideas because they are not rigid algorithms, which makes them very versatile methods that can be adapted to any combinatorial optimization problem and software, yielding results even at the convex optimization level.

D2D-Assisted Multi-User Cooperative Partial Offloading in MEC Based on Deep Reinforcement Learning.

Mobile edge computing (MEC) and device-to-device (D2D) communication can alleviate the resource constraints of mobile devices and reduce communication latency. In this paper, we construct a D2D-MEC framework and study the multi-user cooperative partial offloading and computing resource allocation. We maximize the number of devices under the maximum delay constraints of the application and the limited computing resources. In the considered system, each user can offload its tasks to an edge server and a nearby D2D device. We first formulate the optimization problem as an NP-hard problem and then decouple it into two subproblems. The convex optimization method is used to solve the first subproblem, and the second subproblem is defined as a Markov decision process (MDP). A deep reinforcement learning algorithm based on a deep Q network (DQN) is developed to maximize the amount of tasks that the system can compute. Extensive simulation results demonstrate the effectiveness and superiority of the proposed scheme.

Analysis of the Role of 5G Communication Technology Based on Intelligent Sensor Network in the Construction and Design of the Internet of Things in Free Trade Zones

With the rapid development of the Internet today, the number of various mobile communication terminals has increased rapidly, and 5G has also appeared. With the popularization of 5G technology, new development trends have emerged in more business scenarios. For example, in the 5G era, there will be a lot of room for development in traditional business applications. On this basis, we design a resource allocation that utilizes DQN technology to achieve 5G high-band services. First of all, considering the characteristics of boundary operation, the connection between the base station and the user, the transmission capacity of the base station to the user, and other factors are used as judgment factors, the total energy efficiency is maximized as the goal, and the requirements of mobile users are the constraints. Based on customer service quality assurance, QoS assurance is the object. On the basis of DQN, the convex optimization method is used to solve the given maximum transmission energy between nodes, and DQN is used for iterative iteration to obtain the optimal node and optimal power distribution. Through simulation experiments, the results show that the algorithm has high learning efficiency and convergence and can effectively optimize the allocation of network resources under the premise of ensuring the mobile terminal’s requirements for service quality.

A Load-Balanced and Energy-Efficient Navigation Scheme for UAV-Mounted Mobile Edge Computing

With the development of Unmanned Aerial Vehicles (UAVs) in recent years, UAV-mounted Mobile Edge Computing (MEC) systems are widely used for broadband connectivity and emergency communications in areas without internet. However, the onboard energy of UAVs is limited, and how to provide long-term computing services for ground User Equipments (UEs) still faces significant challenges. In this paper, UAVs are used as mobile base stations to offer MEC services for UEs. Unlike existing solutions that mainly solve UAV path planning from convex optimization methods, we propose a Multi-Agent Path planning (MAP) scheme based on deep reinforcement learning. We aim to minimize the total energy consumption of UAVs while completing the offloading tasks of UEs. At the same time, fairness is taken into account to ensure UE offloading balance and UAV load balance. To this end, we establish the optimization problem and design the state space, action space, and reward function for modeling each UAV through Deep Neural Networks (DNNs). Extensive simulation experiments show that the proposed scheme outperforms other benchmark schemes.

Linesearch Newton-CG methods for convex optimization with noise

This paper studies the numerical solution of strictly convex unconstrained optimization problems by linesearch Newton-CG methods. We focus on methods employing inexact evaluations of the objective function and inexact and possibly random gradient and Hessian estimates. The derivative estimates are not required to satisfy suitable accuracy requirements at each iteration but with sufficiently high probability. Concerning the evaluation of the objective function we first assume that the noise in the objective function evaluations is bounded in absolute value. Then, we analyze the case where the error satisfies prescribed dynamic accuracy requirements. We provide for both cases a complexity analysis and derive expected iteration complexity bounds. We finally focus on the specific case of finite-sum minimization which is typical of machine learning applications.

Complete vehicle energy management using adaptive primal–dual operator splitting

Complete vehicle energy management (CVEM) aims at minimizing the energy consumption of all subsystems inside a vehicle. When the subsystems consist of energy buffers with linear dynamics and/or power converters with quadratic power losses, the CVEM becomes a large-scale and ill-conditioned optimal control problem for which well-known solution approaches (e.g. Pontryagin’s maximum principle, dynamic programming, convex and derivative-free optimization methods) are not effective. In this paper, we design an efficient solution algorithm for this problem by leveraging the framework of operator splitting methods. To facilitate its implementation, we propose a spectral method that automatically tunes the step sizes at every iteration and, in practice, accelerates convergence. Finally, we consider a case study for a parallel-hybrid vehicle and we illustrate the numerical performance of our method by showing that we can efficiently solve a CVEM problem with very large horizons.

Convergence Rates of the Heavy Ball Method for Quasi-strongly Convex Optimization

In this paper, we study the behavior of solutions of the ODE associated to the Heavy Ball method. Since the pioneering work of B.T. Polyak [25], it is well known that such a scheme is very efficient for C2 strongly convex functions with Lipschitz gradient. But much less is known when the C2 assumption is dropped. Depending on the geometry of the function to minimize, we obtain optimal convergence rates for the class of convex functions with some additional regularity such as quasi-strong convexity or strong convexity. We perform this analysis in continuous time for the ODE, and then we transpose these results for discrete optimization schemes. In particular, we propose a variant of the Heavy Ball algorithm which has the best state of the art convergence rate for first order methods to minimize strongly, composite non smooth convex functions.

Finite-Time Output Feedback Robust Controller Based on Tangent Barrier Lyapunov Function for Restricted State Space for Biped Robot

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories.

Convergence results of two-step inertial proximal point algorithm

This paper proposes a two-point inertial proximal point algorithm to find zero of maximal monotone operators in Hilbert spaces. We obtain weak convergence results and non-asymptotic O(1/n) convergence rate of our proposed algorithm in non-ergodic sense. Applications of our results to various well-known convex optimization methods, such as the proximal method of multipliers and the alternating direction method of multipliers are given. Numerical results are given to demonstrate the accelerating behaviors of our method over other related methods in the literature.

Rocket landing guidance using convex optimization and proportional navigation considering performance-limited engine

In recent years, convex optimization has been widely applied in aircraft trajectory optimization and guidance. For rocket vertical landing, the dynamics are highly nonlinear, which easily causes convergence issues in convex optimization. Moreover, for the existing convex optimization methods, it is difficult to implement landing guidance with a performance-limited engine in which the thrust cannot be continuously and instantly regulated. To address these two issues, a novel rocket vertical landing guidance method is developed, in which the guidance in the normal and tangential planes with respect to the rocket velocity is separated to enhance the convergence property of convex optimization. Normal guidance adopts biased proportional navigation to easily satisfy the pinpoint landing with the required attitude angles. For tangential guidance, convex optimization and model predictive control are employed to optimize the thrust command that satisfies the landing velocity limit. Based on this, an impulse equivalent transformation method is designed to derive thrust commands that satisfy the engine limits. Simulation results indicate that the proposed guidance method can achieve precise landing and satisfy various constraints while being highly robust to uncertainties. Moreover, the efficiency, convergence property, and control smoothness are significantly improved.

Energy Saving Strategy of UAV in MEC Based on Deep Reinforcement Learning

Unmanned aerial vehicles (UAVs) have the characteristics of portability, safety, and strong adaptability. In the case of a maritime disaster, they can be used for personnel search and rescue, real-time monitoring, and disaster assessment. However, the power, computing power, and other resources of UAVs are often limited. Therefore, this paper combines a UAV and mobile edge computing (MEC), and designs a deep reinforcement learning-based online task offloading (DOTO) algorithm. The algorithm can obtain an online offloading strategy that maximizes the residual energy of the UAV by jointly optimizing the UAV’s time and communication resources. The DOTO algorithm adopts time division multiple access (TDMA) to offload and schedule the UAV computing task, integrates wireless power transfer (WPT) to supply power to the UAV, calculates the residual energy corresponding to the offloading action through the convex optimization method, and uses an adaptive K method to reduce the computational complexity of the algorithm. The simulation results show that the DOTO algorithm proposed in this paper for the energy-saving goal of maximizing the residual energy of UAVs in MEC can provide the UAV with an online task offloading strategy that is superior to other traditional benchmark schemes. In particular, when an individual UAV exits the system due to insufficient power or failure, or a new UAV is connected to the system, it can perform timely and automatic adjustment without manual participation, and has good stability and adaptability.

Energy‐efficient compressive sensing for multi‐target tracking in wireless visual sensor networks

SummaryWireless visual sensor networks (WVSN) have vital roles in surveillance applications. In these networks, wireless visual sensors include camera and transceiver module and collect visual information. However, energy consumption and coverage of the tracked targets are important challenges in WVSNs since increasing the coverage leads to increasing energy consumption. Therefore, energy optimization and satisfying the quality of experience (QoE) of the tracked targets are essential issues in these networks. In fact, the appropriate focal length setting leads to increasing the target coverage and quality of the captured targets' images and energy consumption. Therefore, selection of the suitable visual sensors and setting their focal length can overcome the energy consumption challenges and improve QoE of the tracked targets. In this case, compressive sensing is also expected to overcome the battery constraints of the WVSN resources. In this paper, the problem is to minimize the energy consumption of the multi‐target tracking with high reliability, while the coverage and also the quality of the received image of the targets are satisfied by selection of the proper visual sensors and the focal length adjustment. The convex optimization method is used to solve the problem. Also, based on the Karush‐Kuhn‐Tucker conditions, the optimal solution for the problem is obtained. Simulation results validate the efficiency of the proposed method in comparison with the other bench mark algorithms.

Fast inertial dynamic algorithm with smoothing method for nonsmooth convex optimization

In order to solve the minimization of a nonsmooth convex function, we design an inertial second-order dynamic algorithm, which is obtained by approximating the nonsmooth function by a class of smooth functions. By studying the asymptotic behavior of the dynamic algorithm, we prove that each trajectory of it weakly converges to an optimal solution under some appropriate conditions on the smoothing parameters, and the convergence rate of the objective function values is $$o\left( t^{-2}\right)$$ . We also show that the algorithm is stable, that is, this dynamic algorithm with a perturbation term owns the same convergence properties when the perturbation term satisfies certain conditions. Finally, we verify the theoretical results by some numerical experiments.

Fast Trajectory Generation Method for Midcourse Guidance Based on Convex Optimization

To generate the midcourse guidance trajectory for intercepting the high-speed and high maneuvering target, which is a strongly nonlinear and strongly constrained problem, a two-stage convex optimization method is proposed to solve the optimal trajectory quickly. In the first stage, an initial trajectory generation method is proposed, by which the trajectory’s terminal state is close to the terminal position. And the generated trajectory is used as the initial solution of the convex optimization method. In the second stage, the original nonconvex optimization problem is transformed into a convex optimization problem by linearization and relaxation methods and then solved discretely. In the numerical simulation, the effectiveness of the proposed method is verified, and the robustness of the method is verified in different initial and terminal states. Then, several ablation experiments are operated to verify the advantage of the rapid initial trajectory generation method in the first stage. Finally, compared with the gauss pseudospectral method (GPM), the proposed method is proved to be efficient and has the potential of online trajectory generation.

Comparison between convex and non-convex optimization methods for collision avoidance maneuvers by a spacecraft

The number of space debris has rapidly increased in the recent times with the rising number of space missions. Thus, to ensure the safety of any operating satellite, collision avoidance maneuvers must be performed. It is also practically impossible to make the state measurements and dynamic models completely error-free. So, this study deals with fuel-optimal collision avoidance maneuvers while also incorporating the effects of uncertainty on them. In this paper, one formulation for convex optimization and another formulation for non-convex optimization have been presented and compared. Effects that the choice of the optimization algorithms and the number of discretization points used have on the optimal Δv as well as on the computational speed have also been discussed.

Online trajectory optimization and guidance algorithm for space interceptors with nonlinear terminal constraints via convex programming

PurposeIn this paper, an online convex optimization method for the exoatmospheric ascent trajectory of space interceptors is proposed. The purpose of this paper is to transform the original trajectory optimization problem into a sequence of convex optimization subproblems.Design/methodology/approachFor convenience in calculating accuracy and efficiency, the complex nonlinear terminal orbital elements constraints are converted into several quadratic equality constraints, which can be better computed by a two-step correction method during the iteration. First, the nonconvex thrust magnitude constraint is convexified by the lossless convexification technique. Then, discretization and successive linearization are introduced to transform the original problem into a sequence of one convex optimization subproblem, considering different flight phases. Parameters of trust-region and penalty are also applied to improve the computation performance. To correct the deviation in real time, the iterative guidance method is applied before orbit injection.FindingsNumerical experiments show that the algorithm proposed in this paper has good convergence and accuracy. The successive progress can converge in a few steps and 3–4 s of CPU time. Even under engine failure or mission change, the algorithm can yield satisfactory results.Practical implicationsThe convex optimization method presented in this paper is expected to generate a reliable optimal trajectory rapidly in different situations and has great potential for onboard applications of space interceptors.Originality/valueThe originality of this paper lies in the proposed online trajectory optimization method and guidance algorithm of the space inceptors, especially for onboard applications in emergency situations.

GPU-Accelerated PD-IPM for Real-Time Model Predictive Control in Integrated Missile Guidance and Control Systems.

This paper addresses the problem of real-time model predictive control (MPC) in the integrated guidance and control (IGC) of missile systems. When the primal-dual interior point method (PD-IPM), which is a convex optimization method, is used as an optimization solution for the MPC, the real-time performance of PD-IPM degenerates due to the elevated computation time in checking the Karush–Kuhn–Tucker (KKT) conditions in PD-IPM. This paper proposes a graphics processing unit (GPU)-based method to parallelize and accelerate PD-IPM for real-time MPC. The real-time performance of the proposed method was tested and analyzed on a widely-used embedded system. The comparison results with the conventional PD-IPM and other methods showed that the proposed method improved the real-time performance by reducing the computation time significantly.

Incentive mechanism for competitive edge caching in 5G-enabled Internet of things

The fifth generation (5G) of cellular networks provides the enabling environment for the Internet of Things (IoT) applications. Hence, the vast proliferation of 5G-enabled IoT devices and services led to an overwhelming growth of data traffic that could saturate the core network’s backhaul links. Nowadays, caching is an unavoidable technique to solve this issue, whereby popular contents are stored on edge nodes near to end-users. There exist several initiatives to motivate caching actors for improving the caching process, but not designed for the real-world competitive caching market. In this work, we propose an incentive caching strategy in a 5G-enabled IoT network by considering a completely competitive caching scenario with multiple 5G mobile network operators (MNOs) and multiple content providers (CPs). The MNOs manage a set of edge caches on their base stations and they are competing to fill these caching resources, while the CPs detain a set of popular contents and are in conflict to rent the MNOs’ caches. Each MNO aims to maximize its monetary profit and offload its backhaul links, as each CP aims to improve the quality of experience (QoE) of its end-users. Then, we formulate a multi-leader multi-follower Stackelberg game to model the interaction between MNOs and CPs and define the different players’ utilities. Subsequently, we propose an iterative algorithm based on the convex optimization method to investigate the Stackelberg equilibrium. Finally, the numerical results of the different experimentations demonstrate that our game-based incentive strategy can significantly alleviate the backhaul links while improving the user QoE.

Synthesis of Modular Subarrayed Phased-Array With Shaped-Beams by Means of Sequential Convex Optimization

In this letter, an efficient method based on sequential convex optimization is proposed to synthesize modular subarrayed phased-arrays with shaped beams. The proposed method consists of two steps. In the first step, the subarray configuration with exact tiling is acquired through solving iterative convex optimization problems. To obtain the arrangement of subarrays with exact tiling, the binary vector sparsity problem is relaxed to be a reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\boldsymbol{l}}_1}$</tex-math></inline-formula> -norm minimization problem which can be solved efficiently by interior point method. In general, there are plenty of exact tiling configurations. To obtain the subarray configuration which is more conductive to radiating the target shaped-beam, the limiting conditions of the shaped-beam are added to the solution process of exact tiling. In the abovementioned solution process, the excitations of the subarrays can be obtained at the same time. However, due to the exact tiling constraints in the solution process, the obtained excitations are usually not the optimal solution for the obtained exact tiling configuration. Therefore, in the second step of the proposed method, the convex optimization method is used again to recompute the excitations of the modular subarrayed phased-array. Two numerical examples are implemented to verify the validity and reliability of the proposed method.