Non-convex Optimization Problem Research Articles

On polling directions for randomized direct-search approaches: application to beam angle optimization in intensity-modulated proton therapy

AbstractDeterministic direct-search methods have been successfully used to address real-world challenging optimization problems, including the beam angle optimization (BAO) problem in radiation therapy treatment planning. BAO is a highly non-convex optimization problem typically treated as the optimization of an expensive multi-modal black-box function which results in a computationally time consuming procedure. For the recently available modalities of radiation therapy with protons (instead of photons) further efficiency in terms of computational time is required despite the success of the different strategies developed to accelerate BAO approaches. Introducing randomization into otherwise deterministic direct-search approaches has been shown to lead to excellent computational performance, particularly when considering a reduced number (as low as two) of random poll directions at each iteration. In this study several randomized direct-search strategies are tested considering different sets of polling directions. Results obtained using a prostate and a head-and-neck cancer cases confirmed the high-quality results obtained by deterministic direct-search methods. Randomized strategies using a reduced number of polling directions showed difficulties for the higher dimensional search space (head-and-neck) and, despite the excellent mean results for the prostate cancer case, outliers were observed, a result that is often ignored in the literature. While, for general global optimization problems, mean results (or obtaining the global optimum once) might be enough for assessing the performance of the randomized method, in real-world problems one should not disregard the worst-case scenario and beware of the possibility of poor results since, many times, it is only possible to run the optimization problem once. This is even more important in healthcare applications where the mean patient does not exist and the best treatment possible must be assured for every patient.

Low-Resolution Optimization for an Unmanned Aerial Vehicle Communication Network under a Passive Reconfigurable Intelligent Surface and Active Reconfigurable Intelligent Surface

This paper investigates the optimization of an unmanned aerial vehicle (UAV) network serving multiple downlink users equipped with single antennas. The network is enhanced by the deployment of either a passive reconfigurable intelligent surface (RIS) or an active RIS. The objective is to jointly design the UAV’s trajectory and the low-bit, quantized, RIS-programmable coefficients to maximize the minimum user rate in a multi-user scenario. To address this optimization challenge, an alternating optimization framework is employed, leveraging the successive convex approximation (SCA) method. Specifically, for the UAV trajectory design, the original non-convex optimization problem is reformulated into an equivalent convex problem through the introduction of slack variables and appropriate approximations. On the other hand, for the RIS-programmable coefficient design, an efficient algorithm is developed using a penalty-based approximation approach. To solve the problems with the proposed optimization, high-performance optimization tools such as CVX are utilized, despite their associated high time complexity. To mitigate this complexity, a low-complexity algorithm is specifically tailored for the optimization of passive RIS-programmable reflecting elements. This algorithm relies solely on closed-form expressions to generate improved feasible points, thereby reducing the computational burden while maintaining reasonable performance. Extensive simulations are created to validate the performance of the proposed algorithms. The results demonstrate that the active RIS-based approach outperforms the passive RIS-based approach. Additionally, for the passive RIS-based algorithms, the low-complexity variant achieves a reduced time complexity with a moderate loss in performance.

Resource management for computational offload in MEC networks with energy harvesting and relay assistance

In mobile edge computing (MEC) networks, the integrated application of energy harvesting (EH) and relay cooperation is a promising technology, which ensures the real-time performance of the system and computing power supply. Relay and EH cooperation also expand communication range and extend the battery life of energy-constrained devices. However, in wireless powered and relay-assisted MEC networks, it is challenging to jointly dispatch energy, and computing resources to coordinate heterogeneous performance requirements. To fill this gap, this paper examines the fundamental compromise between utility energy efficiency (UEE) and stable queue length in wireless powered and relay-assisted MEC network systems, and the amount of data transferred for each unit of energy is called UEE. The data queue and energy queue models are introduced and the constraints of stability of two queues in long term are included in the formulated problem. To tackle the fractional and nonconvex optimization problems, the Dinkelsbach method is utilized. Since optimization problems change from time to time and the long-term averaging queue stability is considered, the Lyapunov optimization theory is introduced to convert the non-convex problems into the solvable one. An online resource offloading allocation algorithm is proposed to determine the solution. In addition, the algorithm implements the control parameter V to achieve the compromise between UEE and stable queue length, while the impact of various parameters are also revealed on system performance.

A constraint qualification for the dislocation hyperbolic augmented Lagrangian algorithm

In this paper, we study an augmented Lagrangian-type algorithm called the Dislocation Hyperbolic Augmented Lagrangian Algorithm (DHALA), which solves an inequality nonconvex optimization problem. We show that the sequence generated by DHALA converges to a Karush-Kuhn–Tucker (KKT) point under the Mangasarian-Fromovitz constraint qualification. The contribution of our work is to consider a constraint qualification into this algorithm. Finally, we present some computational illustrations to demonstrate the performance our algorithm works.

Joint Base Station Selection and Power Allocation Design for Reconfigurable Intelligent Surface-Aided Cell-Free Networks

Cell-free (CF) networks can reduce cell boundaries by densely deploying base stations (BSs) with additional hardware costs and power sources. Integrating a reconfigurable intelligent surface (RIS) into CF networks can cost-effectively increase the capacity and coverage of future wireless systems. This paper considers an RIS-aided CF system where each user is supported by a devoted RIS and can establish connections with multiple BSs for coherent transmission. Specifically, each RIS can enhance signal transmission between users and their selected BSs through passive beam-forming, but also randomly scattered signals from other non-selected BSs to users, causing additional signals and interference in the network. To gain insights into the system performance, we first derive the average signal-to-interference-plus-noise ratio (SINR) received by each user in a closed-form expression. Subsequently, we formulate an optimization problem aimed at maximizing the weighted sum-SINR of all users in the RIS-CF network. This optimization considers both BS transmit power allocation and BS selections as variables to be jointly optimized. To tackle the complexity of this nonconvex optimization problem, we develop an innovative two-layer iterative approach that offers both efficiency and efficacy. This algorithm iteratively updates the transmit power allocation and BS selections to converge to a locally optimal solution. Numerical results demonstrate significant performance improvement for the RIS-CF network using our proposed scheme. These results also highlight the effectiveness of jointly optimizing BS transmit power allocation and BS selections in the RIS-CF network.

A Reentry Trajectory Planning Algorithm via Pseudo-Spectral Convexification and Method of Multipliers

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem, and it constitutes a critical challenge within the field of aerospace engineering. In this paper, an improved sequential convexification algorithm is proposed to solve it and achieve online trajectory planning. In the proposed algorithm, the Chebyshev pseudo-spectral method with high-accuracy approximation performance is first employed to discretize the continuous dynamic equations. Subsequently, based on the multipliers and linearization methods, the original nonconvex trajectory planning problem is transformed into a series of relaxed convex subproblems in the form of an augmented Lagrange function. Then, the interior point method is utilized to iteratively solve the relaxed convex subproblem until the expected convergence precision is achieved. The convex-optimization-based and multipliers methods guarantee the promotion of fast convergence precision, making it suitable for online trajectory planning applications. Finally, numerical simulations are conducted to verify the performance of the proposed algorithm. The simulation results show that the algorithm possesses better convergence performance, and the solution time can reach the level of seconds, which is more than 97% less than nonlinear programming algorithms, such as the sequential quadratic programming algorithm.

Adaptive Dataset Management Scheme for Lightweight Federated Learning in Mobile Edge Computing.

Federated learning (FL) in mobile edge computing has emerged as a promising machine-learning paradigm in the Internet of Things, enabling distributed training without exposing private data. It allows multiple mobile devices (MDs) to collaboratively create a global model. FL not only addresses the issue of private data exposure but also alleviates the burden on a centralized server, which is common in conventional centralized learning. However, a critical issue in FL is the imposed computing for local training on multiple MDs, which often have limited computing capabilities. This limitation poses a challenge for MDs to actively contribute to the training process. To tackle this problem, this paper proposes an adaptive dataset management (ADM) scheme, aiming to reduce the burden of local training on MDs. Through an empirical study on the influence of dataset size on accuracy improvement over communication rounds, we confirm that the amount of dataset has a reduced impact on accuracy gain. Based on this finding, we introduce a discount factor that represents the reduced impact of the size of the dataset on the accuracy gain over communication rounds. To address the ADM problem, which involves determining how much the dataset should be reduced over classes while considering both the proposed discounting factor and Kullback-Leibler divergence (KLD), a theoretical framework is presented. The ADM problem is a non-convex optimization problem. To solve it, we propose a greedy-based heuristic algorithm that determines a suboptimal solution with low complexity. Simulation results demonstrate that our proposed scheme effectively alleviates the training burden on MDs while maintaining acceptable training accuracy.

Reentry trajectory planning for hypersonic vehicles via an improved sequential convex programming method

The reentry trajectory planning problem of hypersonic vehicles is generally a continuous and nonconvex optimization problem. The solution efficiency and convergence properties of the planning algorithm become an essential point when considering the practical application scenarios. In this paper, an augmented-Lagrange-based improved sequential convex programming algorithm is proposed to solve it and achieve superior solutions with higher accuracy and efficiency. Firstly, the mapped Chebyshev pseudo-spectral method is utilized to convert the continuous optimal control problem into a highly approximately discretized one. In this framework, the discretization technique is employed to discretize the states and control variables at the time interval, which leads to the improvement of ill-conditioned differential matrix and better approximation properties of the variables. Moreover, by introducing slack variables, automatically updated penalty parameters and Lagrange multipliers during the convexification processing, the original nonconvex problem is transformed into an augmented-Lagrange-function-formed relaxed convex one. Then, the arrived convex subproblem can be solved iteratively by the matured interior-point method until the predetermined precision is satisfied. Based on this transformation, it can effectively alleviate the numerical difficulty and improve the convergence property of the proposed improved sequential convex programming algorithm. Finally, Rigorous theoretical analysis is conducted to prove that the solution sequence generated by the proposed algorithm could converge to an approximate global solution of the original problem. Numerical simulations are also presented, and it is demonstrated that the solution time of the proposed algorithm is more than 95% less than that of the traditional nonlinear programming methods without losing the merits of high precision.

Joint beamforming and power splitting design for MISO downlink communication with SWIPT: a comparison between cell-free massive MIMO and small-cell deployments

Simultaneous wireless information and power transfer (SWIPT) has been advocated as a highly promising technology for enhancing the capabilities of 5G and 6G devices. However, the challenge of dealing with large propagation path loss poses a significant hurdle. To address this issue, massive multiple-input multiple-output (MIMO) is employed to enhance the efficiency of SWIPT in cellular-based networks with multiple small cells, and especially increase the energy for cell-edge users. In addition, by leveraging a large set of spatially distributed base stations to collaboratively serve SWIPT-enabled user equipment, the cell-free massive MIMO has the potential to provide even better performance than the conventional small-cell systems. In this work, we extend the investigation to include the application of SWIPT technology with alternating current (AC) logic in the cell-free networks and the small-cell networks and propose joint beamforming and power splitting optimization frameworks to maximize the system sum-rate, subject to the constraints on harvested energy, AC logic energy supply, and total transmit power. The optimization problem is shown to be non-convex, posing a significant challenge. To address this challenge, we resort to a two-stage decomposition approach. Specifically, we first introduce quadratic transform-based fractional programming (FP) algorithms to iteratively solve the non-convex optimization problems in the first stage, achieving near-optimal solutions with low time complexities. To further reduce the complexities, we also incorporate conventional schemes such as zero forcing, maximum ratio transmission, and signal-to-leakage-and-noise ratio for the design of beamforming vectors. Second, to determine the optimal power splitting ratio within the framework, we develop a one-dimensional (1-D) search algorithm to tackle the single variable optimization problem reduced in the second stage. These algorithms are then evaluated in the context of cell-free MIMO and small-cell networks with numerical experiments. The results show that the FP-based algorithms can consistently outperform those utilizing the conventional beamforming schemes, and the solutions of this work can achieve up to fivefold improvement in the system sum-rate than the small-cell counterpart while providing different but comparable performance trends in energy harvesting (EH).

Fluorescence molecular tomography based on an online maximum a posteriori estimation algorithm

Fluorescence molecular tomography (FMT) is a non-invasive, radiation-free, and highly sensitive optical molecular imaging technique for early tumor detection. However, inadequate measurement information along with significant scattering of near-infrared light within the tissue leads to high ill-posedness in the inverse problem of FMT. To improve the quality and efficiency of FMT reconstruction, we build a reconstruction model based on log-sum regularization and introduce an online maximum a posteriori estimation (OPE) algorithm to solve the non-convex optimization problem. The OPE algorithm approximates a stationary point by evaluating the gradient of the objective function at each iteration, and its notable strength lies in the remarkable speed of convergence. The results of simulations and experiments demonstrate that the OPE algorithm ensures good reconstruction quality and exhibits outstanding performance in terms of reconstruction efficiency.

A class of accelerated GADMM-based method for multi-block nonconvex optimization problems

A class of accelerated GADMM-based method for multi-block nonconvex optimization problems

Energy-Efficient Access Point Selection Scheme for Reconfigurable-Intelligent-Surface-Assisted Cell-Free Massive MIMO Systems

Reconfigurable intelligent surface (RIS)-assisted cell-free (CF) massive Multiple-Input Multiple-Output (MIMO) technology exhibits significant potential in enhancing the energy efficiency of 6G mobile communications. Nevertheless, recent studies suggest that both access points (APs) and RISs encounter challenges related to a high energy consumption during operation. To address this issue, strategies involving AP hibernation and RIS shut-off are proposed. Subsequently, an optimization problem is formulated to jointly optimize RISs, beamforming vectors, and AP selection with the aim of maximizing the energy efficiency (EE). Initially, the non-convex optimization problem for maximizing energy efficiency is decomposed into three sub-problems. These sub-problems are subsequently reformulated using fractional programming and variational programming techniques and then solved using the successive convex approximation (SCA) algorithm, Dinkelbach algorithm, and greedy algorithm, respectively. Subsequently, an alternate optimization algorithm based on block gradient descent is introduced to iteratively solve the four-variable optimization problem, thereby obtaining an approximate solution to the original problem. The simulation results demonstrate that the algorithm significantly reduces energy consumption. Specifically, compared to the scheme without the hibernation strategy, the energy efficiency (EE) is enhanced by 35%.

Distributed management of energy communities using stochastic profile steering

This paper presents a novel approach for distributed management of energy communities. The proposed method utilizes a stochastic profile steering algorithm as a greedy heuristic. The optimization process considers random parameters such as local forecasted demand, photovoltaic (PV) production, and the initial energy of electric vehicles (EVs) as embedded scenarios. Profile steering coordinates the flexible electricity assets within an energy community by determining the contribution of each prosumer’s profile to the average value of the objective function. It iteratively selects the prosumer that contributes the most until no further improvements can be made. This process scales linearly with the number of controllable prosumers and can achieve various community-level objectives, such as maximizing self-sufficiency or minimizing aggregated cost-of-energy, even when dealing with non-convex optimization problems for modeling each prosumer’s local energy management system. The outcome of the proposed method optimizes the average value of the community’s objective while ensuring that grid limitations are met within a specified probability. The proposed method is evaluated through simulations involving small-scale communities (5 households) and large-scale communities (100 households). The results demonstrate the efficiency, flexibility, and scalability of the proposed method, as well as its ability to reschedule the aggregated demand to ensure that grid limits are not violated with at least a 95% probability.

Golden jackal optimization for economic load dispatch problems with complex constraints

This research paper uses the golden jackal optimization (GJO), a novel meta-heuristic algorithm, to address power system economic load dispatch (ELD) problems. The GJO emulates the hunting behavior of golden jackals. GJO algorithm uses the cooperative attacking behavior of golden jackals to tackle complicated optimization problems efficaciously. The objective of ELD problem is to distribute power system load requirement to the different generators with a minimum total fuel cost of generation. ELD problems are highly complex, non-linear, and non-convex optimization problems while considering constraints namely valve point loading effect (VPL) and prohibited operating zones (POZs). The proposed GJO algorithm is applied to solve complex, non-linear, and non-convex ELD problems. Six different test systems having 6, 10, 13, 40, and 140 generators with various constraints are used to validate the usefulness of the suggested GJO method. Simulation outcomes of the test system are compared with various algorithms reported in the algorithms such as particle swarm optimization (PSO), ant colony optimization (ACO), and backtracking search algorithm (BSA). Results show that the proposed GJO algorithm produces minimal fuel cost and has good convergence in solving ELD problems of power system engineering.

Deep Learning based Model Predictive Controller on a Magnetic Levitation Ball System

The magnetic levitation (maglev) ball system is a prototypical Single-Input-Single-Output (SISO) system, characterized by its pronounced nonlinearity, rapid response, and open-loop instability. It serves as the basis for many industrial devices. For describing the dynamics of the maglev ball system precisely in the pseudo linear model, the long short-term memory (LSTM) based auto-regressive model with exogenous input variables (LSTM-ARX) is proposed. Firstly, the LSTM network is modified by incorporating the auto-regressive structure with respect to sequence input, allowing it to deduce a locally linearized model without the need for Taylor expansion. Then, the LSTM-ARX model is transformed into a linear parameter varying (LPV) state space model, and upon this foundation, a model predictive controller (MPC) is proposed. Specifically, when deducing the MPC, the deep learning-based model is linearized by fixing its state input at the current state, so that the nonlinear, non-convex optimization problem can be converted to a finite-horizon quadratic programming problem, thereby deriving the explicit form of MPC. To further enhance the efficiency of the controller in real-time control tasks, a predictive functional controller (PFC) is proposed. It employs multiple nonlinear functions to fit the control sequence, thereby reducing the number of decision variables of the on-line optimization problem in MPC. The proposed controller was successfully applied to the real-time control of the maglev ball system. Simulation and real-time control experiments have validated the improvement in transient performance and efficiency of the LSTM-ARX model-based PFC (LSTM-ARX-PFC).

Scan-Free and Fully Automatic Tracking of Native Knee Anatomy from Dynamic Stereo-Radiography with Statistical Shape and Intensity Models.

Kinematic tracking of native anatomy from stereo-radiography provides a quantitative basis for evaluating human movement. Conventional tracking procedures require significant manual effort and call for acquisition and annotation of subject-specific volumetric medical images. The current work introduces a framework for fully automatic tracking of native knee anatomy from dynamic stereo-radiography which forgoes reliance on volumetric scans. The method consists of three computational steps. First, captured radiographs are annotated with segmentation maps and anatomic landmarks using a convolutional neural network. Next, a non-convex polynomial optimization problem formulated from annotated landmarks is solved to acquire preliminary anatomy and pose estimates. Finally, a global optimization routine is performed for concurrent refinement of anatomy and pose. An objective function is maximized which quantifies similarities between masked radiographs and digitally reconstructed radiographs produced from statistical shape and intensity models. The proposed framework was evaluated against manually tracked trials comprising dynamic activities, and additional frames capturing a static knee phantom. Experiments revealed anatomic surface errors routinely below 1.0 mm in both evaluation cohorts. Median absolute errors of individual bone pose estimates were below 1.0 or mm for 15 out of 18 degrees of freedom in both evaluation cohorts. Results indicate that accurate pose estimation of native anatomy from stereo-radiography may be performed with significantly reduced manual effort, and without reliance on volumetric scans.

Sum rate maximization for RIS-assisted NOMA-enabled underlay AmBC-CR networks

Ambient backscatter communications (AmBC) have introduced a revolutionary approach to wireless communication that utilizes ambient radio frequency (RF) signals in contrast to self-generated RF signals. This makes AmBC a compelling candidate for future Internet-of-Things (IoT) applications, particularly considering the constraints of energy and spectrum resources. In this work, we investigate a cognitive radio (CR) based underlay network of backscatter devices (BDs) that communicate with the backscatter receiver (BR) by utilizing non-orthogonal multiple access (NOMA). Due to the dual fading effect in backscatter networks, the backscatter link is weakened which degrades the achievable performance. In order to tackle this issue, reconfigurable intelligent surface (RIS) is exploited in such networks. Therefore, to maximize the sum rate of the RIS-assisted NOMA-enabled underlay AmBC-CR (RIS-NUAC) network, subject to individual BDs’ data rate constraint and primary receiver (PR) interference threshold constraint, we jointly optimize the phase shift matrix (PSM) at the RIS and the power reflection coefficients (PRCs) at the BDs. To solve the resultant non-convex optimization problem, we propose a sub-optimal solution based on an alternating optimization (AO) algorithm by applying semidefinite relaxation (SDR) and rank one approximation. Based on simulation results, the proposed scheme demonstrates superior performance over baseline schemes, including NOMA with random phases, NOMA without RIS, orthogonal multiple access (OMA) with optimal phases, and OMA without RIS.

Efficient economic operation based on load dispatch of power systems using a leader white shark optimization algorithm

AbstractThis article proposes the use of a leader white shark optimizer (LWSO) with the aim of improving the exploitation of the conventional white shark optimizer (WSO) and solving the economic operation-based load dispatch (ELD) problem. The ELD problem is a crucial aspect of power system operation, involving the allocation of power generation resources to meet the demand while minimizing operational costs. The proposed approach aims to enhance the performance and efficiency of the WSO by introducing a leadership mechanism within the optimization process, which aids in more effectively navigating the complex ELD solution space. The LWSO achieves increased exploitation by utilizing a leader-based mutation selection throughout each generation of white sharks. The efficacy of the proposed algorithm is tested on 13 engineer benchmarks non-convex optimization problems from CEC 2020 and compared with recent metaheuristic algorithms such as dung beetle optimizer (DBO), conventional WSO, fox optimizer (FOX), and moth-flame optimization (MFO) algorithms. The LWSO is also used to address the ELD problem in different case studies (6 units, 10 units, 11 units, and 40 units), with 20 separate runs using the proposed LWSO and other competitive algorithms being statistically assessed to demonstrate its effectiveness. The results show that the LWSO outperforms other metaheuristic algorithms, achieving the best solution for the benchmarks and the minimum fuel cost for the ELD problem. Additionally, statistical tests are conducted to validate the competitiveness of the LWSO algorithm.

Network sum-rate maximization for network-coded clustered uplink NOMA networks with SWIPT-enabled relays

This paper considers network sum-rate maximization for network-coded clustered uplink non-orthogonal multiple-access (NOMA) networks with simultaneous wireless information and power transfer (SWIPT)-enabled relays. Specifically, the aim is to perform joint power allocation, power-splitting, and relay selection (J-PA-PS-RS), subject to quality-of-service (QoS) requirements. The formulated problem is excessively computationally-intensive, as it is a non-convex optimization problem. To efficiently solve it, it is split into two sub-problems: (1) joint power allocation and power-splitting per relay, and (2) relay selection. Particularly, a solution procedure is proposed, where the joint user and relay power allocation, and power-splitting per relay sub-problem is solved via a low-complexity iterative three-layer algorithm, and then followed by optimal relay selection. Simulation results have revealed that the proposed solution procedure can efficiently be used to maximize the network sum-rate, achieve near-optimal solutions, and outperform other benchmark schemes, while satisfying QoS constraints.

Phase-only beampattern synthesis for maximizing mainlobe gain via Riemannian Newton method

Beampattern synthesis with phase-only weights is extensively utilized in phased-array systems due to the virtue of low-cost and high power efficiency. It is always a non-convex optimization problem having constant modulus constraints (CMCs) and the performance significantly depends on the employed solvers. This paper discusses the phase-only beampattern synthesis for maximizing the mainlobe gain with the constraints on the mainlobe ripple and the relative sidelobe level. As CMC is equivalent to a complex circle manifold, the proposed beampattern synthesis is considered as a manifold optimization problem, and then decomposed into several subproblems under the framework of manifold alternating direction method of multipliers (ADMM). In particular, the subproblem for updating phase-only weights is efficiently tackled by a second-order Riemannian Newton method, which has faster convergence speed and no requirement on line search compared to widely-used first-order Riemannian manifold methods. The explicit convergence condition is derived and the computational complexity is also analyzed. Numerical results show that the proposed method has better performance on the mainlobe gain and sidelobe control accuracy, or less computational cost compared to several representative approaches, such as convex relaxation, standard ADMM, Riemannian gradient descent-based ADMM and Riemannian conjugate gradient methods.