Novel artificial neural network with simulation aspects for solving linear and quadratic programming problems

Ghasabi-Oskoei, H.; Malek, Alaeddin; Ahmadi, Amir Ali

doi:10.1016/j.camwa.2006.10.022

Cited by 12 publications

(2 citation statements)

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“…A number of neural-dynamic models have been proposed, however, according to our previous work [6], the early neural models [13][14] contain finite penalty parameters and generate approximate solutions only. Besides, Lagrange neural network has premature defect when applied to inequalityconstrained QP problems.…”

Section: General Solutions To Static Qpmentioning

confidence: 99%

“…Thus, various dynamic and analog solvers have been developed and investigated with the in-depth research of recurrent neural network (RNN). Owing to its parallel distributed nature and convenience of hardware implementation, the neural-dynamic approach is now regarded as one of the powerful alternatives to real-time computation of QP problems [11] [12].A number of neural-dynamic models have been proposed, however, according to our previous work [6], the early neural models [13][14] contain finite penalty parameters and generate approximate solutions only. Besides, Lagrange neural network has premature defect when applied to inequalityconstrained QP problems.…”

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Performance analysis of LVI-based PDNN applied to real-time solution of time-varying quadratic programming

Zhang

et al. 2014

2014 International Joint Conference on Neural Networks (IJCNN)

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This paper illustrates theoretical analysis and simulative verification on the performance of the linear-variationalinequality based primal-dual neural network (LVI-PDNN), which was designed originally for static quadratic programming (QP) problem solving but is now applied to time-varying QP problem solving. It is theoretically proved that the LVI-PDNN for solving the time-varying QP problem subject to equality, inequality and bound constraints simultaneously could only approximately approach the time-varying theoretical solution, instead of converging exactly. In other words, the steady-state error of the realtime solution can not decrease to zero. In order to better evaluate the time-varying situation, we investigate the upper bound of such an error and the global exponential convergence rate for the LVI-PDNN approaching its loose error bound. Computer simulations further substantiate the performance analysis of the LVI-PDNN exploited for real-time solution of the time-varying QP problem. I. TIME-VARYING QP OF INTERESTQuadratic programming (QP) problems play a significant role in mathematical optimization, and have been theoretically analyzed [1][2] and extensively applied to plenty of scientific fields; e.g., optimal controller design, power-scheduling, digital signal processing, and robot-arm motion planning [3][4]. In the past, researchers usually handle optimization problems only subject to one or two kinds of constraints [5]. In addition, some QP problems are just investigated based on static coefficients (or to say, constant coefficient matrices and vectors) [6], which may not applicative for time-varying cases. Motivated by realtime engineering applications in robotics [5][7], the general time-varying QP (TVQP) in this paper is presented as follows.where Hessian matrix W (t) ∈ R n×n is smoothly timevarying, positive-definite and symmetric at any time instant t ∈ [0, +∞). Besides, coefficient matrices J(t) ∈ R m×n and A(t) ∈ R k×n as well as coefficient vectors q(t) ∈ R n , ξ − (t) ∈ R n , ξ + (t) ∈ R n , d(t) ∈ R m and b(t) ∈ R k are all assumed smoothly time-varying. In time-varying QP (1)-(4), unknown vector x(t) ∈ R n is to be solved in real time t ∈ [0, +∞). II. GENERAL SOLUTIONS TO STATIC QPTo solve the fundamental static QP problem, a lot of methods/algorithms have been proposed [1] [2]. In general, there are two common solutions to such a QP problem. The first one is the numerical algorithms performed on digital computers and it has been widely used to solve small-scale static QP problems. However, when it comes to large-scale real-time applications, in view of its serial-processing nature, such numerical algorithms may result in decline of the performances [8]. Usually, the minimal arithmetic operations are proportional to the cube of Hessian matrix dimension n, which is computationally expensive. As for the second general type of solution, the application of parallel processing has influenced the algorithmic developments [9][10]. Thus, various dynamic and analog solvers have been developed and ...

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Section: General Solutions To Static Qpmentioning

confidence: 99%

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confidence: 99%

Performance analysis of LVI-based PDNN applied to real-time solution of time-varying quadratic programming

Zhang

et al. 2014

2014 International Joint Conference on Neural Networks (IJCNN)

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A Neural Network Model for Solving Nonlinear Optimization Problems with Real-Time Applications

Malek

Yashtini

2009

Advances in Neural Networks – ISNN 2009

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Abstract.A new neural network model is proposed for solving nonlinear optimization problems with a general form of linear constraints. Linear constraints, which may include equality, inequality and bound constraints, are considered to cover the need for engineering applications. By employing this new model in image fusion algorithm, an optimal fusion vector is exploited to enhance the quality of fused images efficiently. The stability and convergence analysis of the novel model are proved in details. The simulation examples are used to demonstrate the validity of the proposed model.

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Ansari

2013

Non-Linear Feedback Neural Networks

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Novel artificial neural network with simulation aspects for solving linear and quadratic programming problems

Cited by 12 publications

References 13 publications

Performance analysis of LVI-based PDNN applied to real-time solution of time-varying quadratic programming

Performance analysis of LVI-based PDNN applied to real-time solution of time-varying quadratic programming

A Neural Network Model for Solving Nonlinear Optimization Problems with Real-Time Applications

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