A new technique for generating quadratic programming test problems

Redundant robot manipulators are usually applied to various complex scenarios where harmful noise especially periodic calculating noise always exists. In order to avoid the task failure affected by the periodic noise, a circadian rhythms neural network (CRNN) is applied to solve motion planning problems of redundant robot manipulators suffering from the periodic noise. First, in this article, we formulate a tracking problem of redundant manipulators as a convex quadratic programming (QP) problem. Second, the QP problem is converted into a matrix equation. Third, based on the neural dynamic design method, a CRNN model is exploited and developed to solve the matrix equation of the tracking problem. Comparative simulations between the proposed CRNN and the traditional zeroing neural network show that the CRNN has better robustness and performance on solving the end-effector tracking task. Two physical experiments are conducted to further certify the effectiveness, robustness, and practicability of the proposed CRNN.

In this paper, we present a recurrent neural network for solving mixed linear complementarity problems (MLCPs) with positive semi-definite matrices. The proposed neural network is derived based on an NCP function and has a low complexity respect to the other existing models. In theoretical and numerical aspects, global convergence of the proposed neural network is proved. As an application, we show that the proposed neural network can be used to solve linear and convex quadratic programming problems. The validity and transient behavior of the proposed neural network are demonstrated by using five numerical examples.

The brain-computer interface (BCI) P300 speller analyzes the P300 signals from the brain to achieve direct communication between humans and machines, which can assist patients with severe disabilities to control external machines or robots to complete expected tasks. Therefore, the classification method of P300 signals plays an important role in the development of BCI systems and technologies. In this article, a novel ensemble support vector recurrent neural network (E-SVRNN) framework is proposed and developed to acquire more accurate and efficient electroencephalogram (EEG) signal classification results. First, we construct a support vector machine (SVM) to formulate EEG signals recognizing model. Second, the SVM formulation is transformed into a standard convex quadratic programming (QP) problem. Third, the convex QP problem is solved by combining a varying parameter recurrent neural network (VPRNN) with a penalty function. Experimental results on BCI competition II and BCI competition III datasets demonstrate that the proposed E-SVRNN framework can achieve accuracy rates as high as 100% and 99%, respectively. In addition, the results of comparison experiments verify that the proposed E-SVRNN possesses the best recognition accuracy and information transfer rate (ITR) compared with most of the state-of-the-art algorithms.

Recently, Ghanbari and Mahdavi-Amiri (Appl Math Model 34:3363–3375, 2010) gave the general compromised solution of an LR fuzzy linear system using ABS algorithm. Here, using this general solution, we solve quadratic programming problems with fuzzy LR variables. We convert fuzzy quadratic programming problem to a crisp quadratic problem by using general solution of fuzzy linear system. By using this method, the crisp optimization problem has fewer variables in comparison with other methods, specially when rank of the coefficient matrix is full. Thus, solving the fuzzy quadratic programming problem by using our proposed method is computationally easier than the solving fuzzy quadratic programming problem by using ranking function. Also, we study the fuzzy quadratic programming problem with symmetric variables. We show that, in this case, the associate quadratic programming problem is a convex problem, and thus, we able to find the global optimal.

An optical reconfigurable intelligent surface (ORIS) was expected to offer extra secrecy performance gain in a visible light communication (VLC) system. However, nonlinear impairments involved degrade the confidential signal reception and have not been fully considered in designing physical layer security (PLS). In this paper, a novel PLS approach is proposed for an ORIS-aided VLC system with consideration of practical nonlinear impairments. It is mathematically formulated to be an optimization problem that maximizes the signal-to-interference-plus-distortion-and-noise ratio of the legitimate link, while entirely suppressing that of multiple eavesdroppers by jointly optimizing the beamforming, jamming and clipping at the transmitters, and also the surface configuration in terms of mirror assignments and rotation angles at the ORIS. We decompose this mixed combinatorial and non-convex optimization problem into three sub-problems and elaborately transform them to be conventional convex programming, quadratic programming and nonlinear programming problems, respectively. Moreover, we also develop a time-efficient iterative approach to achieve the suboptimal solution with low-computational complexity. Simulation results demonstrate the improvement of secrecy performance as compared with conventional schemes, and also the robustness to severe nonlinear impairments and spatial correlation, thereby confirming the beneficial insights of this methodology for secure VLC with nonlinear devices.

: Several algorithms for solving problems in linear, quadratic, and nonlinear programming, network flows, and facilities location were developed and analyzed. Results include: (1) The analysis of the computational complexity of the problem of determining an optimally sparse representation of the null space of a matrix, and the development of worst-case bounds for the shadow-vertex simplex algorithm and several heuristics for distance constrained discrete facility location problems and conditional covering problems; (2) The development of efficient algorithms for dense and sparse assignment problems, strictly convex quadratic programming problems, and a nonlinear programming problem that arises when maximizing a correlation coefficient subject to linear constraints; and (3) The application of iterative methods to large sparse equality-constraind quadratic programs and the development of multiple constraint deletion strategies for active-set algorithms for linearly consrained nonlinear programming problems. (Author)

Based on the global Krotov successive improvement method, we propose a dual computational algorithm for a discrete optimal control problem corresponding to a convex large-scale quadratic programming problem with a separable functional that arises in the prediction of the direct costs (structural) matrix in dynamic input-output models. With decomposition, we are able to use a special form of the constraint matrix to reduce the problem dimension.

Necessary and sufficient conditions are derived, which are fulfilled by quadratic functions that can be written as a product of two affine-linear functions plus an additive constant. This criterium characterizes convex and nonconvex quadratic programming problems, which can be solved by one ofSwarup's [1966a, 1966b, 1966c] algorithm.

Inference on estimators defined by mathematical programming

Let \(T\) be a tree and let \(D\) be the distance matrix of the tree. The problem of finding the maximum of \(x'Dx\) subject to \(x\) being a nonnegative vector with sum one occurs in many different contexts. These include some classical work on the transfinite diameter of a finite metric space, equilibrium points of symmetric bimatrix games and maximizing weighted average distance in graphs. We show that the problem can be converted into a strictly convex quadratic programming problem and hence it can be solved in polynomial time.

The strictly convex quadratic programming problem is transformed to the least distance problem — finding the solution of minimum norm to the system of linear inequalities. This problem is equivalent to the linear least squares problem on the positive orthant. It is solved using orthogonal transformations, which are memorized as products. Like in the revised simplex method, an auxiliary matrix is used for computations. Compared to the modified-simplex type methods, the presented dual algorithm QPLS requires less storage and solves ill-conditioned problems more precisely. The algorithm is illustrated by some difficult problems.

The optimal control problem of linear quadratic regulation (the LQR problem) for linear discrete-time systems with single input delay is studied in this paper. A new and simple approach is applied to derive the optimal control input sequences. With the established duality, we first show that the LQR problem is equivalent to an optimization problem in Krein space. The latter problem is finally converted to a strictly convex quadratic programming problem. Thus we convert the delayed control input into control input delay-free, and convert a dynamic LQR optimal control problem for the linear discrete-time systems into a static mathematical programming model. The optimal control input sequences are successfully derived by solving this strictly convex quadratic programming problem. Our approach is simple and yet very effective in dealing with the LQR problem for the linear discrete-time systems with single input delay.

This paper proposes bounds for the objective function of convex quadratic programming problem (QPP) in general form. The method uses just the eigenvalues of the Hessian matrix. By use of the eigenvalues of the Hessian matrix and solving two simple optimisation problems, we propose an interval which contains the optimal value of QPP. This method can be useful for complicated and large scale optimisation problems as well as for the integer quadratic programming problems and also can be used as a start interval for the other existing mathematical methods for QPP. Another application of the proposed interval is to help the decision maker in real applications to estimate the bounds of the optimal solution. Thus the method is useful from both theoretical and practical approaches. This method can also be applied to solve fractional quadratic programming problems as well as for binary and mixed integer quadratic programming problems. Sensitivity analysis for the objective function is another application of the method which will be discussed. To illustrate the method, several problems are solved.

Aircraft assembly modeling requires mass solving of quadratic programming (QP) problems. Thus, reducing the computation time becomes a very urgent task. Earlier [12], it was shown that a significant reduction in time can be achieved by reformulating the original QP problem in the so-called form of the relative QP problem. The current paper discusses the aspects of using relative QP problem related to the accuracy of the computations. Data preparation for the relative QP problem involves the matrix inversions. Since the Hessian in the considered QP problems is ill-conditioned, this operation leads to a rapid accumulation of roundoff errors. The paper proposes to use the error-free operations of addition and multiplication to increase the accuracy of the QP problem solution and to maintain high computation speed for QP problem solving. Finally, a comparison of the primal, dual, and relative QP problem formulations in terms of computation time and result accuracy for assembly problems is presented.KeywordsQuadratic programmingRelative problem formulationAssembly problemsComputational accuracy

Many physical process systems have performance limitation regardless the input. This limitation usually occurs in the form of input saturation of actuator as the constraint of the system. To overcome this problem, Model Predictive Control (MPC) may be used due to its capability to compute optimal control signal in the presence of input saturation. The optimal control signal is obtained by solving a quadratic programming (QP) problem with variables' constraints at each time instants. QP problem with lower and upper constraint is known to be equivalent to an algebraic loop involving diagonal upper and lower saturation. Hence, QP can be iteratively computed until its solution converges. A slow computation of QP, however, limits its applications for fast systems with simple digital processor. Therefore, in order to be able to be implemented in real-time embedded applications, a fast algorithm of QP solver is in need. In this paper, a comparison study of two QP implementation, i.e. Projected Gauss Seidel (PGS) and so called Algorithm-2, using Arduino Mega 2560 is presented. In this case, MPC with QP solver using both algorithms is implemented to control the speed of lightly loaded BLDC motor. Before implementation, system modeling, controller designing, and simulation are undertaken. The performance of both iterative algorithms are then compared in terms of average computation time in the simulation and implementation. It can be observed from the results that Algorithm-2 gives a bit faster computation than PGS under same conditions.