Convex Optimization Algorithm Research Articles

Optimal control of a solar sail

SummaryOptimal control of a solar sail orbiting around a fixed center of mass is considered. The sail is modelled as a plane surface with two sides having similar optical properties. The control is assumed to be the attitude of the sail and is represented as an element of the projective plane. Mapping this plane into the three dimensional ambient space to compute the actual force generated by a given attitude results in a generally non‐convex set of admissible control values. A suitable convex relaxation is introduced to study the optimality system associated with maximising the change of the sail orbital parameters in a given direction along one orbit. Existence for both the relaxed and the original problems are deduced. Building on previous works, a refined analysis of the control structure is given, proving rigorously that it contains only switchings, and a global bound of the number of switchings is obtained. In order to compute effective solutions, a multiple shooting approach is retained that is well suited for systems with a sequence of switchings between various control subarcs. Three issues are addressed: initialization of shooting by means a tailored semi‐definite relaxation that takes advantage of good convergence properties of modern convex optimization algorithms; changes in the control structure that are accommodated by coupling shooting with differential continuation; implicit character of the Hamiltonian maximization when using Pontrjagin maximum principle that is taken care of by incorporating the associated equation for the dynamical feedback into the shooting procedure. The method is illustrated on an example from NASA for which the sail inclination is optimally changed over one orbital period.

An approximation algorithm for multiobjective mixed-integer convex optimization

An approximation algorithm for multiobjective mixed-integer convex optimization

Relaxed Static Output Feedback Control for Discrete-time Takagi-Sugeno Fuzzy Systems: A Switching Sequence Convex Optimization Algorithm

In this paper, a new switching sequence convex optimization (SSCO) algorithm is proposed for solving non-convex optimization problem with complex time-varying relaxation matrix structures that arises during output feedback design. Firstly, the introduced time-varying relaxation matrix combines the membership functions and the designed switching mechanism to adjust the positive and negative terms of the inequality constraints. As a result, relaxed controller design conditions with complex matrix structures are established. The proposed SSCO algorithm employs switching optimization variables and inner approximation strategy, which is able to compute non-convex optimization problems with complex matrix structures more flexibly and converge quickly. It is worth noting that the implementation of the SSCO algorithm requires a set of strictly feasible initial solutions. Therefore, an initialization iterative algorithm is proposed, which overcomes the difficulties of transforming the solving problem into a typical non-convex optimization problem and linearizing multiple different concave parts, by which a set of optimized feasible solutions are obtained. Finally, simulation examples are used to demonstrate the superiority of the design scheme proposed in this paper.

Robust optimal power flow considering uncertainty in wind power probability distribution

This paper proposes an optimal power flow model that takes into account the uncertainty in the probability distribution of wind power. The model can schedule controllable generators under any possible distribution of wind power to ensure the safe and economic operation of the system. Firstly, considering the incompleteness of historical wind power data, the paper models the uncertainty of wind power using second-order moments of probability distribution and their fluctuation intervals. Subsequently, a robust optimal power flow model based on probability distribution model and joint chance constraints is established. The Lagrangian duality theorem is then employed to eliminate random variables from the optimization model, transforming the uncertainty model into a deterministic linear matrix inequality problem. Finally, a convex optimization algorithm is used to solve the deterministic problem, and the results are compared with traditional chance-constrained optimal power flow model. The feasibility and effectiveness of the proposed method are validated through case study simulations.

A powered descent trajectory planning method with quantitative consideration of safe distance to obstacle

High scientific value areas on celestial bodies such as the Moon and Mars are often located in hazardous terrains. To achieve safe landing exploration, a novel planning method is proposed, which can ensure that the planned trajectory maintains a user-specified distance from obstacles, thus reducing potential collision risk induced by factors such as the body size and model uncertainties. Firstly, the basic model of the trajectory optimization problem and its convexification version is given. The obstacles are modeled as polynomial functions, based on which the “if-then” obstacle avoidance logic explicitly considering the safe distance, is described as a sum of squares constraint. This constraint formulation applies to any obstacle described by a finite number of polynomials, independent of the specific expression of the polynomials (reflecting the shape of the obstacle). Subsequently, the convexification process for the obstacle avoidance constraint is given. Finally, the sequential sum of squares programming problem for the obstacle avoidance trajectory is established, which boils down to a series of semidefinite programming problems. Simulation results show that the closest distance between the planned trajectory and obstacles strictly satisfies the specified distance constraint, and the trajectory could avoid non-convex obstacles. With the promising convergence properties of underlying convex optimization algorithms, advanced autonomous obstacle avoidance guidance schemes are expected to be formed based on the proposed trajectory planning method.

Asynchronous event-triggered guaranteed cost control of uncertain 2-D Markov jump Roesser systems with actuator saturation

This paper investigates the asynchronous event-triggered guaranteed cost control problem for two-dimensional Markov jump Roesser systems with parameter uncertainties and actuator saturation. The hidden Markov model is constructed to characterize the asynchronous phenomenon induced by the mode mismatch between the system and the controller, and a hidden Markov model-based event-triggered mechanism is adopted in controller design to save communication resources. The convex hull representation is employed to process saturated inputs. By using the quadratic Lyapunov function methods and linear matrix inequality techniques, some sufficient criteria are developed to guarantee the asymptotic stability of the addressed system with a guaranteed cost under three different boundary conditions. Finally, a convex optimization algorithm with linear matrix inequality constraints is proposed to design the optimal asynchronous event-triggered guaranteed cost controller, and a numerical example is considered to demonstrate its validity.

An Approach to Maximize the Admitted Device-to-Device Pairs in MU-MIMO Cellular Networks

Due to the shortage of wireless resources and the emergence of a large number of users, determining how to guarantee the quality-of-service (QoS) requirements of users and make more users work in the same spectrum has become an urgent research topic. In this paper, we study a multi-user MIMO (MU-MIMO) cellular network system model in which cellular users (CUs) share the same spectrum resource with multiple device-to-device (D2D) pairs. To maximize the number of admitted D2D pairs sharing the same spectrum with the CUs, a joint power allocation and channel gain (JPACG) algorithm is proposed. The optimization problem is divided into two steps to be solved. First, the power allocation of CUs without D2D pairs admitted is solved. Then, the optimization problem is transformed into minimizing the interference to CUs when CUs are treated as primary users. The admittance order of D2D pairs is determined by the transmission power and channel gain. The proposed algorithm uses a convex optimization algorithm to solve the problem of power allocation joint interference channel gain in order to maximize the number of admitted D2D pairs under the constraints of the signal-to-interference-plus-noise ratio (SINR) threshold and maximum transmission power. In addition, the effect of the number of admitted D2D pairs on the total sum rate of all users is also analyzed. The simulation results show that the proposed JPACG algorithm can achieve better performance in admitting D2D pairs.

On approximating dependence function and its derivatives

Bivariate extreme value distributions can be used to model dependence of observations from random variables in extreme levels. There is no finite dimensional parametric family for these distributions, but they can be characterized by a certain one-dimensional function which is known as Pickands dependence function. In many applications the general approach is to estimate the dependence function with a non-parametric method and then conduct further analysis based on the estimate. Although this approach is flexible in the sense that it does not impose any special structure on the dependence function, its main drawback is that the estimate is not available in a closed form. This paper provides some theoretical results which can be used to find a closed form approximation for an exact or an estimate of a twice differentiable dependence function and its derivatives. We demonstrate the methodology by calculating approximations for symmetric and asymmetric logistic dependence functions and their second derivatives. We show that the theory can be even applied to approximating a non-parametric estimate of dependence function using a convex optimization algorithm. Other discussed applications include a procedure for testing whether an estimate of dependence function can be assumed to be symmetric and estimation of the concordance measures of a bivariate extreme value distribution. Finally, an Australian annual maximum temperature dataset is used to illustrate how the theory can be used to build semi-infinite and compact predictions regions.

A multi-modal vision-language pipeline strategy for contour quality assurance and adaptive optimization

Objective. Accurate delineation of organs-at-risk (OARs) is a critical step in radiotherapy. The deep learning generated segmentations usually need to be reviewed and corrected by oncologists manually, which is time-consuming and operator-dependent. Therefore, an automated quality assurance (QA) and adaptive optimization correction strategy was proposed to identify and optimize ‘incorrect’ auto-segmentations. Approach. A total of 586 CT images and labels from nine institutions were used. The OARs included the brainstem, parotid, and mandible. The deep learning generated contours were compared with the manual ground truth delineations. In this study, we proposed a novel contour quality assurance and adaptive optimization (CQA-AO) strategy, which consists of the following three main components: (1) the contour QA module classified the deep learning generated contours as either accepted or unaccepted; (2) the unacceptable contour categories analysis module provided the potential error reasons (five unacceptable category) and locations (attention heatmaps); (3) the adaptive correction of unacceptable contours module integrate vision-language representations and utilize convex optimization algorithms to achieve adaptive correction of ‘incorrect’ contours. Main results. In the contour QA tasks, the sensitivity (accuracy, precision) of CQA-AO strategy reached 0.940 (0.945, 0.948), 0.962 (0.937, 0.913), and 0.967 (0.962, 0.957) for brainstem, parotid and mandible, respectively. The unacceptable contour category analysis, the (FI,AccI,Fmicro,Fmacro) of CQA-AO strategy reached (0.901, 0.763, 0.862, 0.822), (0.855, 0.737, 0.837, 0.784), and (0.907, 0.762, 0.858, 0.821) for brainstem, parotid and mandible, respectively. After adaptive optimization correction, the DSC values of brainstem, parotid and mandible have been improved by 9.4%, 25.9%, and 13.5%, and Hausdorff distance values decreased by 62%, 70.6%, and 81.6%, respectively. Significance. The proposed CQA-AO strategy, which combines QA of contour and adaptive optimization correction for OARs contouring, demonstrated superior performance compare to conventional methods. This method can be implemented in the clinical contouring procedures and improve the efficiency of delineating and reviewing workflow.

Distributed Primal-Dual Proximal Algorithms for Convex Optimization Involving Three Composite Functions

Distributed Primal-Dual Proximal Algorithms for Convex Optimization Involving Three Composite Functions

Rocket landing guidance based on second-order Picard-Chebyshev-Newton type algorithm

This paper proposes a rocket substage vertical landing guidance method based on the second-order Picard-Chebyshev-Newton type algorithm. Firstly, the continuous-time dynamic equation is discretized based on the natural second-order Picard iteration formulation and the Chebyshev polynomial. Secondly, the landing problem that considers terminal constraints is transformed into a nonlinear least-squares problem with respect to the terminal constraint function and solved with the Gauss-Newton method. In addition, the projection method is introduced to the iteration process of the Gauss-Newton method to realize the inequality constraints of the thrust. Finally, the closed-loop strategy for rocket substage vertical landing guidance is proposed and the numerical simulations of the rocket vertical landing stage are carried out. The simulation results demonstrate that compared with the sequential convex optimization algorithm, the proposed algorithm has higher computational efficiency.

Distributed Newton Step Projection Algorithm for Online Convex Optimization Over Time-Varying Unbalanced Networks

Distributed Newton Step Projection Algorithm for Online Convex Optimization Over Time-Varying Unbalanced Networks

Noise and distortion suppression for industrial confocal microscopy

Industrial confocal microscopy is an optical imaging measurement technology used in the fields of material research, defect detection and industrial inspection. Noise will affect the quality of the image and thus affect its performance. We propose a denoising algorithm based on CNN minimisation in this paper. First, we give the object function of the algorithm and the adaptive calculation formula of the capped value. Then, by using the difference convex (DC) optimisation algorithm framework, the sub-gradient optimisation condition, and the feedback framework, we develop a simple and efficient adaptive-stop iterative optimisation algorithm to solve this model and provide the closed solution of the model at each iteration. The experimental results show that for industrial confocal images, our algorithm can not only effectively suppress noise, but also effectively avoid the distortion of denoised images. The signal-to-noise ratio of industrial confocal denoised images is increased by 1.93 times. In addition, experiments show that the algorithm has good noise reduction ability in other optical imaging instruments, and can suppress not only Gaussian noise, but also Gaussian-Poisson noise.

Solving Constrained Pseudoconvex Optimization Problems with deep learning-based neurodynamic optimization

In this paper, we consider Constrained Pseudoconvex Nonsmooth Optimization Problems (CPNOPs), which are a class of nonconvex optimization problems. Due to their nonconvexity, classical convex optimization algorithms are unable to solve them, while existing methods, i.e., numerical integration methods, are inadequate in terms of computational performance. In this paper, we propose a novel approach for solving CPNOPs that combines neurodynamic optimization with deep learning. We construct an initial value problem (IVP) involving a system of ordinary differential equations for a CPNOP and use a surrogate model based on a neural network to approximate the IVP. Our approach transforms the CPNOP into a neural network training problem, leveraging the power of deep learning infrastructure to improve computational performance and eliminate the need for traditional optimization solvers. Our experimental results show that our approach is superior to numerical integration methods in terms of both solution quality and computational efficiency.

Distributed Integral Convex Optimization-Based Current Control for Power Loss Optimization in Direct Current Microgrids

Due to the advantages of fewer energy conversion stages and a simple structure, direct current (DC) microgrids are being increasingly studied and applied. To minimize distribution loss in DC microgrids, a systematic optimal control framework is proposed in this paper. By considering conduction loss, switching loss, reverse recovery loss, and ohmic loss, the general loss model of a DC microgrid is formulated as a multi-variable convex function. To solve the objective function, a top-layer distributed integral convex optimization algorithm (DICOA) is designed to optimize the current-sharing coefficients by exchanging the gradients of loss functions. Then, the injection currents of distributed energy resources (DERs) are allocated by the distributed adaptive control in the secondary control layer and local voltage–current control in the primary layer. Based on the DICOA, a three-layer control strategy is constructed to achieve loss minimization. By adopting a peer-to-peer data-exchange strategy, the robustness and scalability of the proposed systematic control are enhanced. Finally, the proposed distribution current dispatch control is implemented and verified by simulations and experimental results under different operating scenarios, including power limitation, communication failure, and plug-in-and-out of DERs.

MATLAB-based innovative 3D finite element method simulator for optimized real-time hyperthermia analysis

Background and ObjectiveOwing to the significant role of hyperthermia in enhancing the efficacy of chemotherapy or radiotherapy for treating malignant tissues, this study introduces a real-time hyperthermia simulator (RTHS) based on the three-dimensional finite element method (FEM) developed using the MATLAB App Designer. MethodsThe simulator consisted of operator-defined homogeneous and heterogeneous phantom models surrounded by an annular phased array (APA) of eight dipole antennas designed at 915 MHz. Electromagnetic and thermal analyses were conducted using the RTHS. To locally raise the target temperature according to the tumor's location, a convex optimization algorithm (COA) was employed to excite the antennas using optimal values of the phases to maximize the electric field at the tumor and amplitudes to achieve the required temperature at the target position. The performance of the proposed RTHS was validated by comparing it with similar hyperthermia setups in the FEM-based COMSOL software and finite-difference time-domain (FDTD)-based Sim4Life software. ResultsThe simulation results obtained using the RTHS were consistent, both for the homogeneous and heterogeneous models, with those obtained using commercially available tools, demonstrating the reliability of the proposed hyperthermia simulator. The effectiveness of the simulator was illustrated for target positions in five different regions for both homogeneous and heterogeneous phantom models. In addition, the RTHS was cost-effective and consumed less computational time than the available software. The proposed method achieved 94% and 96% accuracy for element sizes of λ/26 and λ/36, respectively, for the homogeneous model. For the heterogeneous model, the method demonstrated 93% and 95% accuracy for element sizes of λ/26 and λ/36, respectively. The accuracy can be further improved by using a more refined mesh at the cost of a higher computational time. ConclusionsThe proposed hyperthermia simulator demonstrated reliability, cost-effectiveness, and reduced computational time compared to commercial software, making it a potential tool for optimizing hyperthermia treatment.

On convex numerical schemes for inelastic contacts with friction

This paper reviews the different existing Contact Dynamics schemes for the simulation of granular media, for which the discrete incremental problem is based on the resolution of convex problems. This type of discretization has the great advantage of allowing the use of standard convex optimization algorithms. In the case of frictional contacts, we consider schemes based on a convex relaxation of the constraint as well as a fixed point scheme. The model and the computations leading to the discrete problems are detailed in the case of convex, regular but not necessarily spherical particles. We prove, using basic tools of convex analysis, that the discrete optimization problem can be seen as a minimization problem of a global discrete energy for the system, in which the velocity to be considered is an average of the pre- and post-impact velocities. A numerical study on an academic test case is conducted, illustrating for the first time the convergence with order 1 in the time step of the different schemes. We also discuss the influence of the convex relaxation of the constraint on the behavior of the system. We show in particular that, although it induces numerical dilatation, it does not significantly modify the macrosopic behavior of a column collapse en 2d. The numerical tests are performed using the code SCoPI.

Development of a Controlled Dynamics Simulator for Reusable Launcher Descent and Precise Landing

This paper introduces a Reusable Launch Vehicle (RLV) descent dynamics simulator coupled with closed-loop guidance and control (G&C) integration. The studied vehicle’s first-stage booster, evolving in the terrestrial atmosphere, is steered by a Thrust Vector Control (TVC) system and planar fins through gain-scheduled Proportional–Integral–Derivative controllers, correcting the trajectory deviations until precise landing from the reference profile computed in real time by a successive convex optimisation algorithm. Environmental and aerodynamic models that reproduce realistic atmospheric conditions are integrated into the simulator for enhanced assessment. Comparative performance results were achieved in terms of control configuration (TVC-only, fins-only, and both) for nominal conditions as well as with external disturbances such as wind gusts or multiple uncertainties through a Monte Carlo analysis to assess the G&C system. These studies demonstrated that the configuration combining TVC and steerable planar fins has sufficient control authority to provide stable flight and adequate uncertainties and disturbance rejection. The developed simulator provides a preliminary assessment of G&C techniques for the RLV descent and landing phase, along with examining the interactions that occur. In particular, it paves the way towards the development and assessment of more advanced and robust algorithms.

Hybrid distributed online and alternating convex optimization‐based initial value accelerated hybrid precoding for millimeter wave multiple‐input‐multiple‐output

SummaryThe hybrid precoding problem is considered a Frobenius norm reduction problem for the narrowband channel in a millimeter wave (mmWave) with multiple inputs and outputs (mmWave MIMO). This work proposes a hybrid distributed online and alternating convex optimization (HDO‐ACO) algorithm to improve hybrid precoding (HP), interpreted as a trace minimization problem. HDO‐ACO alternately determines the digital and analog precoders to reduce the trace by keeping the other constant. Initially, HDO‐ACO uses Lagrange's method to determine the digital precoding subproblem. Then, it uses the integrated distributed online convex optimization and alternating minimization algorithm in the analog precoder design. In the HP method, the digital and analog precoders are iteratively updated until the highest number of iterations or convergence is reached. But this hybrid precoding method requires an initial analog precoding matrix input to begin the iteration. The algorithms converge gradually and fall into a suboptimal solution when the initial analog precoding matrix is set randomly. Hence, an initial value acceleration‐based heuristic approach is used in the HDO‐ACO alternating minimization algorithm that calculates the initial feasible value of an alternating minimization method using channel conditions. The simulation results of the proposed HDO‐ACO algorithm are presented under bit error rate (BER), spectral efficiency (SE), and convergence behavior by comparing it with modified block coordinate descent–HP (MBCD‐HP), manifold optimization–alternating minimization (MO‐AltMin), and semi‐definite relaxation‐based alternating optimization (SDR‐AO). The proposed HDO‐ACO attains maximum SE and less BER than other hyper‐precoding designs.

DRL-Based Hybrid Task Offloading and Resource Allocation in Vehicular Networks

With the explosion of delay-sensitive and computation-intensive vehicular applications, traditional cloud computing has encountered enormous challenges. Vehicular edge computing, as an emerging computing paradigm, has provided powerful support for vehicular networks. However, vehicle mobility and time-varying characteristics of communication channels have further complicated the design and implementation of vehicular network systems, leading to increased delays and energy consumption. To address this problem, this article proposes a hybrid task offloading algorithm that combines deep reinforcement learning with convex optimization algorithms to improve the performance of the algorithm. The vehicle’s mobility and common signal-blocking problems in the vehicular edge computing environment are taken into account; to minimize system overhead, firstly, the twin delayed deep deterministic policy gradient algorithm (TD3) is used for offloading decision-making, with a normalized state space as the input to improve convergence efficiency. Then, the Lagrange multiplier method allocates server bandwidth to multiple users. The simulation results demonstrate that the proposed algorithm surpasses other solutions in terms of delay and energy consumption.