Quadratic Programming Problem Research Articles

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 %.

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.

Ultrafast Hybrid Computing Systems Enabled by Memristor‐Based Quadratic Programming Circuits

AbstractImplementing algorithms purely on digital computing platforms dramatically halts the performance of conventional computing systems. Revolutionary computing systems with extreme energy efficiency and high accuracy are demanded to handle the growing computing tasks. Here, the research on hybrid analog–digital computing platforms enabled by memristor‐based optimization solvers for achieving ultrafast computations is presented. By utilizing tunable memristors as parameters to solve linear programming (LP) and quadratic programming (QP) problems, a real‐time control algorithm for micro air vehicles (MAVs) and a support vector machine (SVM) algorithm for cancer diagnosis are implemented. These experiments demonstrate over 2000x speed‐up compared to conventional digital platforms, with negligible energy consumption, using a memristor‐based system consisting of six memristors. These findings underscore the vast potential of memristor‐based optimization solvers not only in hybrid analog–digital computing platforms but also as a transformative solution for a wide range of modern computing challenges. This approach promises significant advancements in energy efficiency and ultrafast speed, positioning it as a leading contender for next‐generation computing paradigms.

Robust adaptive beamforming for cylindrical uniform conformal arrays based on low-rank covariance matrix reconstruction

Recently, conformal arrays have attracted considerable interest because such arrays can provide reduced radar cross-section and increased angle coverage. In this article, we devise a robust adaptive beamforming (RAB) approach using cylindrical uniform conformal array (CUCA). Firstly, we derive the minimum variance distortionless response (MVDR) beamformer for the CUCA by utilizing the noise subspace of interference covariance matrix (ICM) and steering vector (SV) of the signal-of-interest (SOI). Subsequently, the ICM is reconstructed by estimating the noise-free covariance matrix of the CUCA outputs and the interference projection matrix. Specifically, the noise-free covariance matrix can be regarded as multiple low-rank covariance matrices, and each low-rank matrix is reconstructed by formulating a nuclear norm minimization (NNM) problem. With the reconstructed covariance matrix, the 2-D DOAs of sources are determined by employing 2-D MUSIC spectrum to form the interference projection matrix. In addition, the SOI SV is estimated by solving a quadratically constrained quadratic programming (QCQP) problem. Numerical results demonstrate that the proposed approach is obviously superior to the existing RAB techniques.

Virtually coupled train set control subject to space-time separation: A distributed economic MPC approach with emergency braking configuration

The emerging virtual coupling technology aims to operate multiple train units in a Virtually Coupled Train Set (VCTS) at a minimal but safe distance. To guarantee collision avoidance, the safety distance should be calculated using the state-of-the-art space-time separation principle that separates the Emergency Braking (EB) trajectories of two successive units during the whole EB process. In this case, the minimal safety distance is usually numerically calculated without an analytic formulation. Thus, the constrained VCTS control problem is hard to address with space-time separation, which is still a gap in the existing literature. To solve this problem, we propose a Distributed Economic Model Predictive Control (DEMPC) approach with computation efficiency and theoretical guarantee. Specifically, to alleviate the computation burden, we transform implicit safety constraints into explicitly linear ones, such that the optimal control problem in DEMPC is a quadratic programming problem that can be solved efficiently. For theoretical analysis, sufficient conditions are derived to guarantee the recursive feasibility and stability of DEMPC, employing compatibility constraints, tube techniques and terminal ingredient tuning. Moreover, we extend our approach with globally optimal and distributed online EB configuration methods to shorten the minimal distance among VCTS. Finally, experimental results demonstrate the performance and advantages of the proposed approaches.

Solving inverse boundary value problem of Poisson equation by LS-SVM

Abstract In this paper, a new method based on least squares support vector machines (LS-SVM) is presented for solving the inverse boundary value problem of Poisson equation. The closed form analytical solution is obtained by optimizing the regression parameters. The core problem is to transform the parametric regression problem into a quadratic programming problem. To demonstrate the efficiency of the proposed algorithm, numerical experiments are conducted. The proposed method is found to be feasible for the inverse boundary value problem of Poisson equation.

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

Safety-critical anti-disturbance control of tugs for collaborative berthing

It is a challenging task for large ships themselves berthing in port areas even for an experienced captain. This paper addresses the collaborative berthing by utilizing tugs maneuvering at low speeds for operating a ship. A safety-critical anti-disturbance control method is proposed for collaborative berthing subject to the contact force constraint, velocity constraints, ship constraints referring to constraining the tugs velocities in the body frame of the ship and the angular rate of the ship, as well as ocean disturbances. First, a finite-time kinematic control law is developed for each tug to track the desired position and heading prescribed by using the relative distance between two tugs and the heading of port shoreline. Next, an extended state observer (ESO) based on robust exact differentiator (RED) is used for each tug to estimate the model uncertainties and environment disturbances. Then, a safety-critical anti-disturbance control law is designed for each tug by employing an RED-based ESO. Finally, through converting the contact force constraint and ship constraints to velocity constraints on tugs, a quadratic programming problem is solved to obtain the collaborative velocity signals for achieving the collaborative operation of the connected tugs subject to velocity constraints. It is proven that the closed-loop control system is finite-time input-to-state stable and the safety during collaborative berthing can be guaranteed in the presence of environmental disturbances. Simulation results are given to substantiate the efficacy of the proposed safety-critical anti-disturbance control method of tugs for collaborative berthing.

Two-Step Quadratic Programming for Physically Meaningful Smoothing of Longitudinal Vehicle Trajectories

Longitudinal vehicle trajectories suffer from errors and noise because of detection and extraction techniques, challenging their applications. Existing smoothing methods either lack physical meaning or cannot ensure solution existence and uniqueness. To address this, we propose a two-step quadratic programming method that aligns smoothed speeds and higher-order derivatives with physical laws, drivers’ behaviors, and vehicle characteristics. Unlike the well-known smoothing splines method, which minimizes a weighted sum of discrepancy and roughness in a single quadratic programming problem, our method incorporates prior knowledge of position errors into two sequential quadratic programming problems. Step 1 solves half-smoothed positions by minimizing the discrepancy between them and raw positions, subject to physically meaningful bounds on speeds and higher-order derivatives of half-smoothed positions. Step 2 solves smoothed positions by minimizing the roughness while maintaining physically meaningful bounds and allowing the deviations from raw data of smoothed positions by at most those of the half-smoothed positions and prior position errors. The second step’s coefficient matrix is not positive definite, necessitating the matching of the first few smoothed positions with corresponding half-smoothed ones, with equality constraints equaling the highest order of derivatives. We establish the solution existence and uniqueness for both problems, ensuring their well-defined nature. Numerical experiments using Next Generation Simulation (NGSIM) data demonstrate that a third-order derivative constraint yields an efficient method and produces smoothed trajectories comparable with manually re-extracted ones, consistent with the minimum jerk principle for human movements. Comparisons with an existing approach and application to the Highway Drone data set further validate our method’s efficacy. Notably, our method is a postprocessing smoothing technique based on trajectory data and is not intended for systematic errors. Future work will extend this method to lateral vehicle trajectories and trajectory prediction and planning for both human-driven and automated vehicles. This approach also holds potential for broader smoothing problems with known average error in raw data. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: The authors extend their gratitude to the Pacific Southwest Region University Transportation Center and the University of California Institute of Transportation Studies (UC ITS) Statewide Transportation Research Program (STRP) for their valuable financial support.

A verified training support vector machine in bearing fault diagnosis

Abstract The combination of support vector machine (SVM) and deep learning is widely used in bearing fault diagnosis. The SVM-based bearing fault diagnosis method usually uses features extracted from bearing vibration signals as input. However, environmental noise in industrial applications can affect the feature representation, potentially leading to failures in SVM-based fault diagnosis methods. Adversarial robustness verification methods can evaluate the robustness of models to small perturbations in feature representations. Certified defense methods achieve robustness enhancement by embedding adversarial robustness verification into the learning process of the model. Thus, we propose a certified defense method named verified training SVM (VT-SVM) based on Lagrange duality. The proposed method incorporates adversarial robustness verification into the SVM learning framework, thereby enhancing the robustness of SVM in noisy environments. First, the certified defense optimization problem of SVM is constructed by combining the original optimization problem of SVM with the adversarial robustness verification problem. Then, the certified defense optimization problem is converted into an equivalent convex quadratic programming problem by introducing slack variables. Next, the Lagrange duality is used to transform the convex quadratic programming problem into a dual problem. Finally, the solution to the original optimization problem can be obtained by solving the dual problem. We validate the effectiveness of VT-SVM on the artificial dataset, the rolling bearing dataset from Case Western Reserve University, and the VBL-VA001 dataset from Sepuluh Nopember Institute of Technology. Experimental results demonstrate that our method both ensures high predictive performance and improves the resistance of the model to small noise.