A Neural Network for Solving Nonlinear Programming Problems

In this paper, we present a highperformance dynamic optimization scheme to solve a class of fractional programming (FP) problems. The main idea is to convert the FP problem into an equivalent convex second-order cone programming problem. A neural network model based on a dynamic model is then constructed for solving the obtained convex programming problem. By employing a credible Lyapunov function approach, it is shown that the proposed neural network model is stable in the sense of Lyapunov and is globally convergent to an exact optimal solution of the original optimization problem. A block diagram of the model is also given. Several illustrative examples are provided to show the efficiency of the proposed method in this manuscript.

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“…Employing (1) and using (12)- (14), the FP problem (10) and (11) is modified into an equivalent CSOCP as…”

Section: Casementioning

confidence: 99%

A practical nonlinear dynamic framework for solving a class of fractional programming problems

Nazemi

Tahmasbi

2015

Nonlinear Dyn

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“…Given the strong ability of approximation, neural network (NN) has been utilized by some researchers to solve the nonlinear optimization (NLP) problem. In the work of Chen et al, 47 NN is proposed for solving convex nonlinear programming problems. Additionally, Xue et al 48 construct a project NN for solving degenerate quadratic programming problems with general linear constraints.…”

Section: Introductionmentioning

confidence: 99%

Robust model predictive control of uncertain nonlinear time‐delay systems via control contraction metric technique

Duan

Wei

Xie

2021

Intl J Robust & Nonlinear

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This article is concerned with the problem of robust model predictive control (MPC) for uncertain nonlinear time‐delay systems. In order to reduce the computational conservativeness of the existing robust MPC given in the min–max optimization formulation, a novel tube‐based MPC method is investigated via exploring MPC and control contraction metric (CCM) technique. Based on the Kyapunov–Krasovskii arguments, the MPC is designed as a nominal controller to generate a reference trajectory. By constructing a functional formulation of the inner product on tangent space, the CCM technique is applied to develop a local ancillary controller to guarantee the actual trajectory being contained within a robust invariant tube. In addition, to alleviate the burden of computing geodesic in the design of CCM technique, we propose a direct method using the neural network to search for the minimal geodesic online. By employing the sequential quadratic programming algorithm, this method improves the efficiency of online calculation with high accuracy. Finally, numerical simulation is employed to validate the effectiveness of the proposed method.

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“…In fact, there have been various types of neural networks proposed for solving linear programming, nonlinear programming, variational inequalities, etc., we cite for example [7][8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

A neural network for solving a convex quadratic bilevel programming problem

Zhong

Wan

2010

Journal of Computational and Applied Mathematics

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a b s t r a c tA neural network is proposed for solving a convex quadratic bilevel programming problem. Based on Lyapunov and LaSalle theories, we prove strictly an important theoretical result that, for an arbitrary initial point, the trajectory of the proposed network does converge to the equilibrium, which corresponds to the optimal solution of a convex quadratic bilevel programming problem. Numerical simulation results show that the proposed neural network is feasible and efficient for a convex quadratic bilevel programming problem.

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A Neural Network for Solving Nonlinear Programming Problems

Cited by 32 publications

References 22 publications

A practical nonlinear dynamic framework for solving a class of fractional programming problems

A practical nonlinear dynamic framework for solving a class of fractional programming problems

Robust model predictive control of uncertain nonlinear time‐delay systems via control contraction metric technique

A neural network for solving a convex quadratic bilevel programming problem

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