Quadratic Programming Problem Research Articles

A subgradient projection method for quasiconvex multiobjetive optimization

We discuss a subgradient projection method for dealing with the nonconvex nonsmooth multiobjective optimization problem when every component of the vector-valued function is strongly quasiconvex in the sense of Polyak [Existence theorems and convergence of minimizing sequences in extremum problems with restrictions. Soviet Math. 1966;7:72–75]. Under mild assumptions, we ensure that the generated sequence converges to an efficient solution point of the multiobjective optimization problem and we provide a kind of linear convergence rate. The algorithm is based on a specific generalized subdifferential that was recently introduced for strongly quasiconvex functions, this approach provides new and valuable information on the generated sequence and its convergent point. Finally, we present numerical experiments for classes of quadratic fractional programming problems.

Optimal coordination of directional overcurrent relays: A fast and precise quadratically constrained quadratic programming solution methodology

AbstractNowadays, power system protection is increasingly important because of the growing number of customers and the pressing need for timely fault resolution and relay operations. This paper addresses the non‐linear nature of the objective function in the optimal coordination of directional overcurrent relays (DOCRs) by employing a quadratic Taylor series expansion around an operating point, converting the problem into a quadratically constrained quadratic programming problem, ensuring a global optimal solution with increased computational efficiency. Additionally, the quadratic constraints are converted into second‐order cone constraints for compatibility with the CPLEX solver. Using the least square method, the operating point values are determined and further fine‐tuned using iterations with the DOCR operation times. The IEEE 3‐bus, IEEE 8‐bus, and IEEE 14‐bus test systems are used to test the method, which shows higher improvement rates in reducing DOCR operation times and enhancing cooperation than conventional and metaheuristic methods. The simulation results verify the numerical superiority of the method in optimizing the protection system's efficiency while obtaining rapid and accurate solutions. The proposed method was tested on IEEE 3‐bus, 8‐bus, and 14‐bus systems, optimizing relay operating times to 0.87, 2.96, and 7.05 s, respectively, demonstrating the method's efficiency over conventional approaches.

An adaptive variable-parameter dynamic learning network for solving constrained time-varying QP problem

To efficiently solve the time-varying convex quadratic programming (TVCQP) problem under equational constraint, an adaptive variable-parameter dynamic learning network (AVDLN) is proposed and analyzed. Being different from existing varying-parameter and fixed-parameter convergent-differential neural network (VPCDNN and FPCDNN), the proposed AVDLN integrates the error signals into the time-varying parameter term. To do so, the TVCQP problem is transformed into a time-varying matrix equation. Second, an adaptive time-varying design formulation is designed for the error function, and then, the error function is integrated into the time-varying parameter. Furthermore, the AVDLN is designed with the adaptive time-varying design formulation. Moreover, the convergence and robustness theorems of AVDLN are proved by Lyapunov stability analysis, and Mathematical analysis demonstrates that AVDLN possesses a smaller upper bound on the convergence error and a faster error convergence rate than FPCDNN and VPCDNN. Finally, the validity of AVDLN is demonstrated by simulations, and the comparative results prove that the proposed AVDLN has a faster convergence speed and smaller error fluctuation.

Gradient-based differential neural network to time-varying constrained quadratic programming

This paper introduces a novel approach to solving time-varying quadratic programming (TVQP) problems with time-dependent constraints, using gradient-based differential neural networks (GDNN). We establish the theoretical framework for both conventional gradient neural networks (CGNN) and GDNN models, highlighting their effectiveness in addressing dynamic optimization challenges. Comparative theoretical analyses show that the proposed GDNN model achieves higher accuracy than the CGNN model, significantly reducing solution errors with exponential convergence. Moreover, the use of a sign-bi-power activation function (SBPAF) ensures reasonable convergence times for the GDNN model. Our approach is validated through simulations of TVQP problems under specific constraints. The results demonstrate that while both models are capable of solving these problems, the GDNN model outperforms the CGNN model in minimizing optimization errors (residual errors), especially when varying the scaling factor γ, the GDNN model also shows superior performance and more efficient convergence.

Minimum jerk motion planning for maritime autonomous surface ships based on Bézier curves

Maritime collisions are a leading cause of accidents at sea, causing severe casualties, economic losses, and environmental damage. Although numerous methods have been developed to mitigate collisions, existing research primarily emphasises decision-making and path planning, often overlooking motion planning methods that incorporate dynamic constraints and ship-specific kinematics. This paper presents a motion planning method that takes into account ship dynamics to minimise jerk, the acceleration change rate, during ship acceleration and deceleration. The paper demonstrates the differential flatness property of the 3-DOF ship motion model, which allows for the direct use of flat outputs to implement motion planning and facilitate the addition of dynamic constraints. The front-end path search is performed using the traditional A* algorithm. To represent the trajectory as a piecewise Bézier curve, we use the Bernstein polynomial basis function. Based on this curve, we propose a motion planning method that employs jerk as the cost function and includes necessary constraints. This transforms the problem into a typical convex quadratic programming problem, ensuring the solvability of the optimisation problem. Finally, simulations are carried out to evaluate the effectiveness of the proposed method.

Optimizing Renewable Strategies for Emission Reduction Through Robotic Process Automation in Smart Grid Management

The integration of renewable energy into Intelligent Distribution Networks (IDNs) is challenged by the inherent variability and fluctuations in energy supply, particularly with photovoltaic (PV) generation as the primary form of distributed generation (DG). However, managing the fluctuations and variability in renewable energy supply presents significant challenges. To address these complexities, it is vital to optimally coordinate flexible resources from source–network–storage–load (SNSL) in a manner that aligns with cross-sectoral emission reduction strategies while enhancing grid stability and efficiency. This paper addresses these challenges by proposing a strategy that optimizes the coordination of PV-based DG, storage, and load resources through Robotic Process Automation (RPA) to enhance grid stability and support emissions reduction. We use a two-layer dispatching framework: the lower-layer model, formulated as a quadratic programming problem, maximizes PV utilization for individual users, while the upper-layer model, based on a second-order cone relaxation approach, manages the overall IDN to minimize operational costs. The iterative solution leverages tie-line power flow as boundary information to ensure convergence across the network. Validated on an enhanced IEEE 33-bus system, the approach demonstrates a 62% increase in PV-based DG consumption and a 25% reduction in active power losses, highlighting its potential to improve grid efficiency and contribute to emission reduction goals.

A hierarchical intersection system control framework in mixed traffic conditions

Signalized intersections play a crucial role in urban road system and are a significant source of vehicle delays. Conventional intersection control methods struggle to cope with increasingly challenging traffic conditions. Fortunately, the development of artificial intelligence(AI), information communication technology(ICT) and connected and automated vehicle(CAV) technologies has brought new opportunities to enhance traffic performance at intersections. Based on these technologies, in the mixed traffic environment of CAVs and connected human-driven vehicles (CHVs), this paper proposes a hierarchical intersection system control framework, which adopts intersection level distributed control and corridor level centralized control. At the intersection level, considering the impact of CAV-dedicated lanes and using the CAV platoon and “1 + n” platoon consisting of one leading CAV and n following CHVs as control units, the mixed integer quadratic programming problem and optimal control problem are formulated to collaboratively optimize signal timing, lane settings and vehicle trajectories at isolated signalized intersections. At the corridor level, based on the optimization results of the intersection level and the critical path information, the critical path performance function and multi-stage optimal trajectory control formula are constructed to optimize the signal offsets and vehicle trajectories, which are passed to the intersection level, and ultimately minimize vehicle delays in the corridor. Simulation experiments and sensitivity analysis demonstrate the effectiveness and stability of the proposed framework in reducing vehicle delay and improving fuel consumption.

Quadratic Programming Problems and Its Solution Techniques With Neural Network Modeling

ABSTRACTThis paper presents a study on quadratic programming problems (QPP) and introduces a new neural network model with feasibility analysis. The stability analysis of QPP using neural network modeling is also discussed. The proposed neural network model has a simple form, and its optimal feasibility for both primal and dual QP problems is established. The model demonstrates a good convergence rate with a minimal number of iterations, achieving a very fast convergence to the exact solutions of both the primal and dual QP problems. The optimal solutions for the original QP problem and its dual QPP are obtained. Finally, two simple numerical examples are simulated to illustrate the findings.

Static actuator-sharing algorithm for concurrent control of multiple plasma properties

Abstract Simultaneous regulation of multiple properties in next-generation tokamaks like ITER and Fusion Pilot Plant (FPP) may require the integration of different plasma control algorithms. Such integration requires the conversion of individual controller commands into physical actuator requests while accounting for the coupling between different plasma properties. This work proposes a tokamak and scenario-agnostic actuator-sharing algorithm (ASA) to perform the above-mentioned command-request conversion and, hence, integrate multiple plasma controllers. The proposed algorithm implicitly solves a quadratic programming (QP) problem formulated to account for the saturation limits and the relation between the controller commands and physical actuator requests. Since the constraints arising in the QP program are linear, the proposed ASA is highly computationally efficient and can be implemented in the tokamak plasma control system (PCS) in real time. Furthermore, the proposed algorithm is designed to handle real-time changes in the control objectives and actuators’ availability. Nonlinear simulations carried out using the Control Oriented Transport SIMulator (COTSIM) illustrate the effectiveness of the proposed algorithm in achieving multiple control objectives simultaneously.

Fix and bound: an efficient approach for solving large-scale quadratic programming problems with box constraints

Fix and bound: an efficient approach for solving large-scale quadratic programming problems with box constraints

Longitudinal and Lateral Cooperative Control of Preview Intelligent Vehicles with Stabilization

Aiming at the highly nonlinear and coupled longitudinal and transverse motion control problems of intelligent vehicle path tracking control, a new method of preview MPC path tracking control is proposed by combining visual preview model and model predictive control theory. The method first locally linearizes the nonlinear prediction model and transforms the MPC optimization solution problem into a quadratic programming problem. The longitudinal vehicle speed and the preview distance are then treated as known in each control time domain, an exponential model is applied to characterize the longitudinal vehicle speed, and a transverse angular velocity-center of mass lateral deflection (r-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r-\\beta $$\\end{document}) phase plane plot is applied to characterize the vehicle stability. Finally, proportional integral differential stability controller is designed to improve vehicle stability. Simulation and test results show that: Compared with the MPC tracking control method, the preview MPC control method proposed in this paper can optimize the vehicle tracking performance on different adhesion coefficient road surfaces and improve the tracking accuracy, and this enhancement effect is more obvious at high speeds.

A weighted hybrid indoor positioning method based on path loss exponent estimation

With the rapid development of the Internet of Things (IoT), location-based services (LBS) have gained significant attention due to their widespread applications in daily life. This paper addresses the indoor target positioning problem in wireless sensor networks (WSNs). A weighted constrained linear least squares algorithm based on path loss exponent estimation (PLE-WCLLS) with received signal strength (RSS) and angle of arrival (AoA) hybrid measurements is proposed. To address the challenges of unknown transmission power and path loss exponent (PLE), the proposed method employs a linear least squares (LLS) estimation approach based on the ranging maximum likelihood (ML) estimation model to estimate both parameters. Subsequently, a confidence weight adjustment strategy is designed to reduce positioning errors. To handle the highly non-convex and nonlinear nature of the RSS/AoA hybrid optimization model, a linearization method based on Taylor series expansion is presented. Accurate target position estimation is achieved by solving a constrained quadratic programming problem. The effectiveness of the proposed algorithm is validated through numerical simulations and experimental evaluation in a real indoor environment. Compared to traditional positioning methods, the PLE-WCLLS algorithm improves positioning accuracy by 13.2%, and it performs exceptionally well even in scenarios with fewer sensor nodes. This gives it broad application prospects in areas such as IoT device management, personnel tracking in smart buildings, and asset localization in industrial automation.

Directional differentiability of the optimal value function in quadratic programming problem on Hilbert spaces

Directional differentiability of the optimal value function in quadratic programming problem on Hilbert spaces

Gust load alleviation of a flexible flying wing with linear parameter-varying modeling and model predictive control

This paper presents a practical model predictive control (MPC) framework for gust load alleviation of a flexible flying wing. Both the controller solving and state estimation are based on a reduced-order model, which features a linear parameter-varying (LPV) form, avoiding online linearization and reducing the scale of the corresponding quadratic programming problem. An improved modeling and model reduction process is used to enhance modeling efficiency and ensure that the reduced-order model can accurately capture the rigid-flexible coupled characteristics of the flexible flying wing under arbitrary gusts. By reconstructing the output of the control-oriented model to include both rigid-body motion and flexible vibrations, the rigid-flexible coupled multi-objective control is established as an MPC problem for reference tracking. The online optimization is formulated in a sparse fashion and combined with an iterative algorithm based on predicted trajectories, describing the variation of model dynamics within the prediction horizon more accurately. With a time-varying Kalman estimator for state updating, the closed-loop simulations are performed for gust alleviation performance validation. Additionally, the real-time potential of the proposed MPC framework is demonstrated through Monte Carlo simulations.

Divisional intuitionistic fuzzy least squares twin SVM for pipeline leakage detection

Improving the accuracy of pipeline leak detection in noisy environments is significant for maintaining pipeline safety. Currently, the weighted support vector machine (SVM) is extensively employed. Among them, Intuitionistic fuzzy twin SVM (IFTSVM) has good robustness due to the integration of intuitionistic fuzzy set theory. However, IFTSVM does not fully consider the position information of samples in the feature space, cannot reduce the impact of heterogeneous clustering noise. Moreover, it requires solving two quadratic programming problems (QPPs), which is inefficient. To address the aforementioned issues, this paper proposes a divisional intuitionistic fuzzy least squares twin SVM (DIFL-TSVM) for pipeline leakage detection. This approach proposes a novel divisional intuitionistic fuzzy membership calculation strategy to reduce the impact of heterogeneous clustering noise and simplify the calculation of sample membership. In addition, DIFL-TSVM transforms the original QPPs into two linear equations using the least squares method to improve the efficiency of model. This paper verifies that the DIFL-TSVM model not only has the ability to eliminate the effects of discrete noise and heterogeneous clustering noise but also more efficiency on water supply pipeline leakage diagnosis experiments and UCI datasets. The experimental results show that DIFL-TSVM has higher leak identification with a detection accuracy of 95.6 %.

Systematic MPC tuning with direct response shaping: Parameterization and Inverse optimization-based Tuning Approach (PITA)

The automatic tuning of the weighting parameters in model predictive control (MPC) requires a systematic strategy to shape the state and input responses to become close to the user’s specifications. In this paper, based on the system-level parameterization of controllers, the system response under MPC is considered as the optimized response matrix under the tuning parameters, and hence an inverse optimization formulation is proposed to seek the tuning under which the desired response is close to being optimal. This results in a two-phase procedure, both formulated as quadratic programming (QP) or linear programming (LP) problems. First, the user specifications are interpreted as “reference” responses or hard constraints, under which the closest realizable response is found. Then, by fitting the realizable response to optimality conditions, the inversely optimal MPC parameters are determined with minimum residuals. The proposed automatic MPC tuning approach is generic and efficient, whose practical performance is demonstrated by applications on single-loop and process unit-level models.

Hybrid TBETI domain decomposition for huge 2D scalar variational inequalities

AbstractThe unpreconditioned H‐TFETI‐DP (hybrid total finite element tearing and interconnecting dual‐primal) domain decomposition method introduced by Klawonn and Rheinbach turned out to be an effective solver for variational inequalities discretized by huge structured grids. The basic idea is to decompose the domain into non‐overlapping subdomains, interconnect some adjacent subdomains into clusters on a primal level, and enforce the continuity of the solution across both the subdomain and cluster interfaces by Lagrange multipliers. After eliminating the primal variables, we get a reasonably conditioned quadratic programming (QP) problem with bound and equality constraints. Here, we first reduce the continuous problem to the subdomains' boundaries, then discretize it using the boundary element method, and finally interconnect the subdomains by the averages of adjacent edges. The resulting QP problem in multipliers with a small coarse grid is solved by specialized QP algorithms with optimal complexity. The method can be considered as a three‐level multigrid with the coarse grids split between primal and dual variables. Numerical experiments illustrate the efficiency of the presented H‐TBETI‐DP (hybrid total boundary element tearing and interconnecting dual‐primal) method and nice spectral properties of the discretized Steklov–Poincaré operators as compared with their finite element counterparts.

Support vector machine based on the quadratic unconstrained binary optimization model

Abstract Support vector machine (SVM) is a powerful supervised machine learning model that is often used in binary classification algorithms. As Moore’s Law approaches its theoretical limits and the demand for machine learning to handle large-scale, high-dimensional data analysis intensifies, the necessity of adopting non-traditional computational approaches becomes evident. Quantum computing, in particular, emerges as a vital solution for the effective training of SVM models, providing capabilities beyond those of classical computing systems. To solve the above problems, a QUBO (quadratic unconstrained binary optimization) model is proposed to transform the SVM machine learning model into a quadratic unconstrained binary optimization problem so that they can be effectively trained on the D-Wave platform using adiabatic quantum computer. The results show that the QUBO model can transform the SVM model into a simple quadratic programming problem, which makes it suitable for adiabatic quantum computer processing. When processing large-scale and high-dimensional data, this transformation shows a natural advantage and significantly improves computational efficiency. The application potential of this transformation technology is huge in the medical field.

Global optimization for large‐scale water network synthesis based on dynamic partition and adaptive bound tightening

AbstractThe synthesis of large‐scale integrated water networks is typically formulated as nonconvex mixed‐integer quadratic constrained programming (MIQCP) or QCP problems. With the complexity arising from bilinear terms in modeling mass flows of contaminants and binary variables representing the presence of units or streams, numerous local optima exist, thus presenting a significant optimization challenge. This study introduces a deterministic global optimization algorithm based on mixed‐integer programming (MIP) to tackle such problems. The approach involves dynamically strengthening the relaxed problems to converge towards the original problems. A simultaneous partition strategy is proposed combining locally uniform division with dynamic partitioned variables choosing. Furthermore, several adaptive bound contraction schemes are introduced to efficiently manage the size of the relaxed problems, assisting in accelerating the solution process. The algorithm's effectiveness and robustness are demonstrated with a large test set, showing superior performance compared to commercial solvers specifically on MIQCP problems.

Model-less optimal visual control of tendon-driven continuum robots using recurrent neural network-based neurodynamic optimization

Tendon-driven continuum robots (TDCRs) have infinite degrees of freedom and high flexibility, posing challenges for accurate modeling and autonomous control, especially in confined environments. This paper presents a model-less optimal visual control (MLOVC) method using neurodynamic optimization to enable autonomous target tracking of TDCRs in confined environments. The TDCR’s kinematics are estimated online from sensory data, establishing a connection between the actuator input and visual features. An optimal visual servoing method based on quadratic programming (QP) is developed to ensure precise target tracking without violating the robot’s physical constraints. An inverse-free recurrent neural network (RNN)-based neurodynamic optimization method is designed to solve the complex QP problem. Comparative simulations and experiments demonstrate that the proposed method outperforms existing methods in target tracking accuracy and computational efficiency. The RNN-based controller successfully achieves target tracking within constraints in confined environments.