Quadratic Programming Problem Research Articles

Neighbor-based joint spatial division and multiplexing in massive MIMO: user scheduling and dynamic beam allocation

AbstractTwo-stage precoding schemes have been developed to reduce the channel estimation overhead in FDD systems. By integrating user scheduling into these schemes, it becomes possible to meet the quality-of-service requirements of high-density wireless communication systems, despite the limitations on spatial resources and transmit power budget. In this paper, we propose a user scheduling and dynamic beam allocation method for neighbor-based joint spatial division multiplexing (N-JSDM) transmission. The user scheduling problem is formulated as a 0–1 quadratic programming problem to maximize effective spectral efficiency (ESE) using directional channel properties. To address the complexity issue, convex relaxation and linearization methods are employed to transform the problem into a 0–1 mixed integer linear programming, and a dimensionality reduction method is introduced. The proposed user scheduling-aided N-JSDM scheme reduces downlink training length and feedback of channel state information. Additionally, a dynamic configuration form is used for pre-beamforming matrix design based on user distribution, outperforming conventional approaches. Simulation results demonstrate higher ESE achieved by the proposed scheme compared to previous methods.

Distributed Collaborative Control of Redundant Robots Under Weight-Unbalanced Directed Graphs

In consideration of the limitation of the communication and the possibility that redundant robots might deliver information at different power levels, cases under weight-unbalanced directed graphs from the network topology perspective are in larger accordance with those in multiple redundant robot systems. By moving forward along this direction, a distributed controller is proposed in this paper to handle circumstances of collaborative control of multiple redundant robots under weight-unbalanced directed graphs. This kind of control problem is modelled into generalized quadratic programming (QP) problems with equality and inequality constraints. Then, the above QP problems are solved by a proposed neural-dynamics-based method, whose stability and convergence are theoretically proved subsequently. Besides, several experimental examples are conducted, and related comparisons are provided to demonstrate the feasibility of the proposed controller.

Learning Cost Functions for Reinforced Learned Controllers in a Quadrupedal Robot

In this work, we will consider a reinforced learning controller developed for a quadrupedal robot and we learn for which cost function such a controller is an optimal control. In particular, we will transform the learning problem into a quadratic programming problem and solve it to obtain the learned cost function. Our approach is based on second-order Lagrangian mechanics since we will use that an optimal control problem is equivalent to a second-order variational problem. We also obtain error bounds for the approximation of the cost function.

Graph Evolution-Based Vertex Extraction for Hyperspectral Anomaly Detection.

Anomaly detection is a fundamental task in hyperspectral image (HSI) processing. However, most existing methods rely on pixel feature vectors and overlook the relational structure information between pixels, limiting the detection performance. In this article, we propose a novel approach to hyperspectral anomaly detection that characterizes the HSI data using a vertex-and edge-weighted graph with the pixels as vertices. The constructed graph encodes rich structural information in an affinity matrix. A crucial innovation of our method is the ability to obtain internal relations between pixels at multiple topological scales by processing different powers of the affinity matrix. This power processing is viewed as a graph evolution, which enables anomaly detection using vertex extraction formulated as a quadratic programming problem on graphs of varying topological scales. We also design a hierarchical guided filtering architecture to fuse multiscale detection results derived from graph evolution, which significantly reduces the false alarm rate. Our approach effectively characterizes the topological properties of HSIs, leveraging the structural information between pixels to improve anomaly detection accuracy. Experimental results on four real HSIs demonstrate the superior detection performance of our proposed approach compared to some state-of-the-art hyperspectral anomaly detection methods.

Neutrosophic parametric study of piecewise quadratic fuzzy multi-objective dynamic programming problems

The goal of this research is to investigate fuzzy multiobjective dynamic programming issues with fuzzy parameters in the objective functions and single valued trapezoidal neutrosophic numbers in the left hand side of the constraints. Piecewise quadratic fuzzy numbers characterize these fuzzy parameters. In addition, applying the score function of the neutrosophic numbers to convert the constraints parameters into its crisp . Some basic notions in the problem under the pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique is presented for obtaining a subset of the parametric space that has the same pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

МЕТОДЫ НЕЛИНЕЙНОГО ПРОГРАММИРОВАНИЯ В РЕШЕНИИ КОНЕЧНЫХ ИГР

The paper considers the formulation of nonlinear programming problems for finding a Nash equilibrium situation in a bimatric game and in a game with three participants. An overview of existing methods for solving is given: an algorithm for solving bimatric LemkeHowson games, methods for solving quadratic and convex programming problems for a finite game with three participants.

Notice of Violation of IEEE Publication Principles: Sequential Convex Programming for Collaboration of Connected and Automated Vehicles

Notice of Violation of IEEE Publication Principles<BR><BR>"Sequential Convex Programming for Collaboration of Connected and Automated Vehicles," <BR>by Xiaoxue Zhang, Jun Ma, Zilong Cheng, Frank L. Lewis, and Tong Heng Lee, <BR>in IEEE Transactions on Intelligent Vehicles, Early Access <BR><BR>After careful and considered review of the content and authorship of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE’s Publication Principles. <BR><BR>This paper contains significant portions of original text from the paper cited below. The original text was copied without attribution (including appropriate references to the original author(s) and/or paper title) and without permission. <BR><BR>"Networked Model Predictive Control for Vehicle Collision Avoidance" <BR> by Bassam Alrifaee, <BR>in RWTH Aachen University, Dissertation, 04 May 2017 <BR>BR>"Sequential convex programming MPC for dynamic vehicle collision avoidance" <BR>by Bassam Alrifaee, Janis Maczijewski, Dirk Abel, <BR>in the Proceedings of the IEEE Conference on Control Technology and Applications, 2017, pp. 2202-2207 <BR><BR> <br/> This paper investigates the collaboration of multiple connected and automated vehicles (CAVs) in different scenarios. In general, the collaboration of CAVs can be formulated as a nonlinear and nonconvex MPC problem. Most of the existing approaches available for utilization to solve such an optimization problem suffer from the drawback of considerable computational burden, which hinders the practical implementation in real time. This paper proposes the use of SCP, which is a powerful approach to solving the nonlinear and nonconvex MPC problem in real time. To appropriately deploy the methodology, as a first stage, SCP requires linearization and discretization when addressing the nonlinear dynamics of the system model adequately. Based on the linearization and discretization, the original MPC problem can be transformed into a QCQP problem. Besides, SCP also involves convexification to handle the associated nonconvex constraints. Thus, the nonconvex QCQP can be reduced to a quadratic programming (QP) problem that can be solved rather quickly. Therefore, the computational efficiency is suitably improved despite the existence of nonlinear and nonconvex characteristics, whereby the implementation is realized in real time. Furthermore, simulation results in three different scenarios of autonomous driving are presented to validate the effectiveness and efficiency of our proposed approach.

Novel Snap-Layer MMPC Scheme via Neural Dynamics Equivalency and Solver for Redundant Robot Arms With Five-Layer Physical Limits.

To obtain smoother kinematic control of minimum motion, a novel snap-layer minimum motion scheme, otherwise known as the minimum motion planning and control (MMPC) scheme for redundant robot arms, is proposed for the first time in this study. With the primary task of tracking planned paths and the consideration of satisfying five-layer physical limits, the snap-layer MMPC problem is transformed into a quadratic programming (QP) problem. Five-layer physical limits include angle-layer, velocity-layer, acceleration-layer, jerk-layer, and snap-layer limits, which are all considered and then transformed into a unified-layer bounded constraint through Zhang neural dynamics (ZND) equivalency. Furthermore, the snap-layer performance index and equation constraint are derived by utilizing the ZND formula. Therefore, the proposed snap-layer MMPC scheme is formulated as a standard QP that can avoid the potential physical damage of redundant robot arms. The snap-layer projection neural dynamics (PND) solver is presented and used to acquire the neural solution of the QP. Simulation results on a 6-degrees-of-freedom (DOF) planar redundant robot arm are presented to substantiate the effectiveness and superiority of the proposed snap-layer MMPC scheme by comparing it with the jerk-layer MMPC scheme and the minimum snap norm (MSN) scheme.

Dynamic origin-destination matrix estimation for networks operating under free-flow conditions using macroscopic flow dynamics

The origin-destination (OD) matrix is a crucial requirement for efficient transportation planning, however its estimation still remains one of the most challenging tasks in transportation. This paper proposes a novel methodology for the estimation of dynamic OD matrices. The proposed methodology integrates disaggregated measurements from stationary sensors, e.g. loop detectors, with a macroscopic model that associates OD demands with Traffic counts on specific network links. We investigate networks that operate under free-flow conditions, hence the dynamic OD matrix estimation problem is formulated as a linear mathematical program. Finally, we reformulate the problem to obtain a computationally cheap quadratic programming problem that allows real-time estimation of OD matrices within the time-window under study. We demonstrate the effectiveness of our methodology through a literature network, showcasing its ability to accurately capture travel patterns in a computationally efficient manner, allowing informed decision-making processes in transportation planning and management.

Evaluation of Grid Support Capacity From Electrified Railways

High power level and temporal operation flexibility endow electric trains with great potential for improving grid resilience. It becomes crucial to quantify the grid support capacity (GSC) from large-scale electrified railways. This paper innovatively proposes a hierarchical train coordination and trajectory regulation method to evaluate and deliver the GSC from electrified railways. In the light of the mechanical energy consumption analysis of train running, the energy-oriented train operation model is proposed to avoid the nonlinear differential dynamics of train kinetics when coordinating large-scale trains. Then the aggregation and disaggregation of trains for grid support can be formulated as linear and convex quadratic programming problems respectively. To closely follow the reference power and enhance the feasibility of train operation, a novel iterative discretization approach is proposed to generate the precise reference trajectory. A sliding mode controller with disturbance bound adaption is devised to overcome the modeling errors and disturbances when deploying GSC in realistic environment. Comprehensive numerical examples verify the effectiveness of the proposed scheme, and demonstrate the significant grid support potential from collaborative electrified railways.

A new global algorithm for homogeneous complex quadratic programming problems and applications

A new global algorithm for homogeneous complex quadratic programming problems and applications

Achieving Emission-Reduction Goals: Multi-Period Power-System Expansion Under Short-Term Operational Uncertainty

Stochastic adaptive robust optimization is capable of handling short-term uncertainties in demand and variable renewable-energy sources that affect investment in generation and transmission capacity. We build on this setting by considering a multi-year investment horizon for finding the optimal plan for generation and transmission capacity expansion while reducing greenhouse gas emissions. In addition, we incorporate multiple hours in power-system operations to capture hydropower operations and flexibility requirements for utilizing variable renewable-energy sources such as wind and solar power. To improve the computational performance of existing exact methods for this problem, we employ Benders decomposition and solve a mixed-integer quadratic programming problem to avoid computationally expensive big-M linearizations. The results for a realistic case study for the Nordic and Baltic region indicate which investments in transmission, wind power, and flexible generation capacity are required for reducing greenhouse gas emissions. Through out-of-sample experiments, we show that the stochastic adaptive robust model leads to lower expected costs than a stochastic programming model under increasingly stringent environmental considerations.

Numerical solution of box constrained separable convex quadratic programming problems

In this paper, minimization problems with a separable convex quadratic objective function subject to a linear equality constraint/linear equality constraints, and bounds on the variables (box constraints) are considered. A necessary and sufficient condition for a feasible solution to be an optimal solution to each of these problems has been established. A convergent polynomial algorithm for solving the problem with a linear equality constraint and bounded variables is proposed, and some numerical results, obtained by this algorithm, are presented.

Economic Model Predictive Control in Buildings Based on Piecewise Linear Approximation of Predicted Mean Vote Index

Energy shortage is a challenge for many countries, and building energy consumption accounts for a considerable proportion of global energy consumption. The main work of this paper is to optimize the energy consumption of heating, ventilating, and air conditioning (HVAC) systems in buildings based on economic model predictive control (EMPC). The cost in EMPC design includes energy consumption and predicted mean vote (PMV), which is an index that evaluates the thermal comfort of indoor occupants. In order to model the nonlinearity of the PMV index, we propose a lattice piecewise linear (PWL) approximation, which has high approximation precision and facilitates the resulting optimization problem, which is basically a piecewise quadratic programming problem. For the piecewise quadratic programming, we propose a descent algorithm that converges quickly and scales well with the length of the prediction horizon in the EMPC problem. The experimental results demonstrate that the proposed method saves 19.78% of the electricity cost compared to the conventional control strategy and significantly increases indoor comfort. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> — The motivation of this article is to provide a control strategy to reduce building energy consumption and ensure indoor thermal comfort. In most of the existing methods for air conditioning temperature control, the occupants’ comfort hasn’t been considered. In this paper, thermal comfort is described by the PMV index, which is basically nonlinear. In order to model the thermal comfort more accurately, in this paper, the PMV index is approximated piecewise linearly in order to meet the requirements of accuracy and computational efficiency. The resulting optimization problem is not hard to solve, and we provide an efficient algorithm for solving this optimization problem. Preliminary simulation experiments demonstrate that this approach is practical, i.e., it achieves energy reduction and ensures thermal comfort. Our strategy, however, has not yet been deployed in real buildings. In future research, we will propose similar techniques for large-scale systems in order to solve energy optimization problems containing multiple thermal zones and realize the proposed technique in real buildings.

Multi-objective Feed Reservoir Control via Optimal Pump Scheduling

Pumping acid mine drainage water from source to the feed reservoir that feeds the eMalahleni Water Reclamation Plant, using fixed-speed pumps, in an optimal manner takes the form of a mixed-integer quadratic programming problem. A simulation study is presented where the most optimal pumping schedule is determined using a differential evolution algorithm. The pumping schedule has to adhere to feed reservoir level constraints while minimizing composition fluctuations. The optimized pumping schedule leads to overall stabilization of the feed reservoir composition and level, which has a direct benefit to the operation of the processing plant.

Data-Driven Model Predictive Control for Uncalibrated Visual Servoing

This paper addresses the image-based visual servoing (IBVS) control problem with an uncalibrated camera, unknown dynamics, and constraints. A novel data-driven uncalibrated IBVS (UIBVS) strategy is proposed, incorporated with the Koopman-based model predictive control (KMPC) algorithm and the adaptive robust Kalman filter (ARKF). First, to alleviate the need for calibration of the camera’s intrinsic and extrinsic parameters, the ARKF with an adaptive factor is utilized to estimate the image Jacobian matrix online, thereby eliminating the laborious camera calibration procedures and improving robustness against camera disturbances. Then, a data-driven MPC strategy is proposed, wherein the unknown nonlinear dynamic model is learned using the Koopman operator theory, resulting in a linear Koopman prediction model. Only input–output data are used to construct the prediction model, and hence, the proposed approach is robust against model uncertainties. Furthermore, with a symmetric quadratic cost function, the proposed approach solves the quadratic programming problem online, and visibility constraints as well as joint torque constraints are taken into account. As a result, the proposed KMPC scheme can be implemented in real time, and the UIBVS performance degradation which arises from the control torque constraints can be avoided. Simulations and comparisons for a 2-DOF robotic manipulator demonstrate the feasibility of the proposed approach. Simulation results further validate that the computation time of the proposed approach is comparable to the one of kinematic-based methods.

Privileged multi-view one-class support vector machine

One-class support vector machine (OCSVM) is a typical one-class classification approach, which learns the classifier by using only the target samples. At present, most OCSVM works hypothesize that the samples have only one view, while multi-view OCSVM has not been taken into account. In this paper, a novel multi-view one-class support vector machine method with privileged information learning (MOCPIL) is put forward. MOCPIL embodies both the consensus principle and complementarity principle in multi-view learning. Privileged information is additional data that is available only in the training process, but not in the testing process. By introducing the idea of privileged information learning, MOCPIL implements the complementarity principle by treating one view as the training data and the other view as the privileged data. Moreover, MOCPIL implements the consensus principle by requiring that different views of the same object should give similar predicting outputs. The learning problem of MOCPIL is a quadratic programming (QP) problem, which is able to be solved by off-the-shelf QP solvers. To the best of our knowledge, this is the first study to tackle the multi-view learning problem based on OCSVM. The performance of MOCPIL is evaluated through extensive experiments. The experimental results have shown that MOCPIL explicitly outperforms the existing multi-view one-class classification methods.

Modern algorithm of linear and quadratic programming in optimization and problems of deformation of structures of variable structure in contact conditions

Various mathematical problems, in which the goal of finding the extremum of a functional is set, belong to the problems of mathematical programming and optimization problems. Practically directed problems of finding the optimal solution are extremely numerous in economics, management, technology, and others. They are related to increasing production efficiency, reducing resource costs, improving design solutions and technological processes, reducing mass, dimensions, etc. Among them, an important role is given to the methods of limiting the maximum stresses caused by external loads. Solving such problems begins with mathematical formalization. Constructive, economic or technological indicators are chosen as variation parameters. The search for the best solution is reduced to the selection of a set of parameters that provide a stationary value of the objective function. Extreme problems of practical orientation contain equality-inequality constraints in mathematical models. In improving the technical characteristics of machines, a significant role belongs to engineering and technical workers, who find optimal options at the design stage. At the same time, an essential element of the design process is the modeling of the determining processes in structures, taking into account the main influencing factors and behavior scenarios. Optimization is an important area of applied mathematics that provides effective tools for such modeling. Universal Algorithm is proposed in work [3] – a numerous scheme for solving quadratic programming (QP) problems for calculating the optimal point of a wide range of applied problems. At the same time, the linear programming (LP) problem is considered as a partial case of the (QP) problem. That is, in the universal algorithm for setting 2 optimization problems, they are formalized in a single and convenient form of symmetric matrix dependence, which makes it possible to build a single effective algorithm based on matrix algebra operations. In particular, it allows you to consider the practical tasks of calculating VAT in constructions of a variable structure consisting of separate parts connected by one-way connections. The main goal of this work is to analyze the behavior of the algorithm when increasing the number of constraints of the inequality type, to refine the computational scheme, and to formulate conclusions. Two model problems are considered as examples of the algorithm. This is a classic "transport" problem of LP and the behavior of a model of a bridge structure with one-way connections in cables under variations of wind loads. The number of ropes has been increased to 20, and the limits of one-way connections to 40.

First/second-order predefined-time convergent ZNN models for time-varying quadratic programming and robotic manipulator application

Zeroing neural network (ZNN) model, an important class of recurrent neural network, has been widely applied in the field of computation and optimization. In this paper, two ZNN models with predefined-time convergence are proposed for the time-varying quadratic programming (TVQP) problem. First, in the framework of the traditional ZNN model, the first-order predefined-time convergent ZNN (FPTZNN) model is proposed in combination with a predefined-time controller. Compared with the existing ZNN models, the proposed ZNN model is error vector combined with sliding mode control technique. Then, the FPTZNN model is further extended and the second-order predefined-time convergent ZNN (SPTZNN) model is developed. Combined with the Lyapunov method and the concept of predefined-time stability, it is shown that the proposed FPTZNN and SPTZNN models have the properties of predefined-time convergence, and their convergence time can be flexibly adjusted by predefined-time control parameters. Finally, the proposed FPTZNN and SPTZNN models are compared with the existing ZNN models for the TVQP problem in simulation experiment, and the simulation experiment results verify the effectiveness and superior performance of the proposed FPTZNN and SPTZNN models. In addition, the proposed FPTZNN model for robot motion planning problem is applied and successfully implemented to verify the practicality of the model.

DIRECTIONAL DIFFERENTIABILITY OF THE OPTIMAL VALUE IN QUADRATIC PROGRAMMING PROBLEMS UNDER LINEAR CONSTRAINTS ON HILBERT SPACES

We investigate the first-order directional differentiability of the optimal value function in parametric quadratic programming problems under linear constraints in Hilbert spaces. We derive an explicit formula for computing the directional derivative of the optimal value function in cases where the quadratic part of the objective function is in Legendre form.