A novel neural network based on NCP function for solving constrained nonconvex optimization problems

Effati, Sohrab; Moghaddas, Mohammad

doi:10.1002/cplx.21673

Cited by 4 publications

(11 citation statements)

References 57 publications

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“…Table reports the comparison results in terms of solution, CPU time, and l 2 ‐norm error with four different initial points. It can be seen that the proposed neural network not only has a better performance in solution accuracy but also has faster convergence rate than the models in Xia et al () and Effati and Moghaddas (). It is also found that the Xia et al's model is unstable and can not solve this example.…”

Section: Simulation Resultsmentioning

confidence: 88%

“…The proposed neural network , Xia et al's model , and the Effati and Moghaddas's model are compared in Table in terms of solution, CPU time, and l 2 ‐norm error with four different initial points. From Table , it can be observed that the proposed neural network has a better performance in convergence time than the models in Xia et al () and Effati and Moghaddas (). It is also seen that the proposed model is more accurate in terms of solution and l 2 ‐norm error than other models.…”

Section: Simulation Resultsmentioning

confidence: 89%

“…To illustrate that the new current neural network is more efficient, the maximum clique problem and the network utility maximization (NUM) problem are analyzed by the neural network . To show further the accuracy of the neural network , the comparisons are made with two models in Xia et al () and Effati and Moghaddas (), through the following examples. Xia et al introduced the following dynamic system for solving NCNO problem :

\frac{d}{d t} ((), \begin{matrix} center \\ array x (t) \\ array μ (t) \end{matrix}) = s ([], \begin{matrix} array - x + {(x)}^{+} - \nabla f ({(x)}^{+}) - \nabla g ({(x)}^{+}) {(μ)}^{+} \\ array - μ + {(μ)}^{+} + (g ({(x)}^{+}) - b) \end{matrix}),

where ( x ) + =( x 1 + ,…, x n + ) T , ( μ ) + =( μ 1 + ,…, μ m + ) T ,

{x_{i}}^{+} = \max ({}, 0, x_{i})

{μ_{i}}^{+} = \max ({}, 0, μ_{i})

, and s >0 is a designing constant.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Xia et al introduced the following dynamic system for solving NCNO problem :

\frac{d}{d t} ((), \begin{matrix} center \\ array x (t) \\ array μ (t) \end{matrix}) = s ([], \begin{matrix} array - x + {(x)}^{+} - \nabla f ({(x)}^{+}) - \nabla g ({(x)}^{+}) {(μ)}^{+} \\ array - μ + {(μ)}^{+} + (g ({(x)}^{+}) - b) \end{matrix}),

where ( x ) + =( x 1 + ,…, x n + ) T , ( μ ) + =( μ 1 + ,…, μ m + ) T ,

{x_{i}}^{+} = \max ({}, 0, x_{i})

{μ_{i}}^{+} = \max ({}, 0, μ_{i})

, and s >0 is a designing constant. In addition, we consider a gradient‐based neural network model (Effati & Moghaddas, ) for solving whose state variable is given by the following dynamic system:

\frac{d w false(t false)}{d t} = - κ \nabla ((), \frac{1}{2} {(‖‖, normalΦ false(w false))}^{2}), w false(t_{0} false) = w_{0},

where

w = ((), x, μ_{p}) \in X \times {double-struckR}_{+}^{m}

normalΦ false(x, μ_{p} false) = false({false(\nabla_{x} L_{p} false(x, μ_{p} false) false)}^{T}, false(scriptZ false(x, μ_{p} f...

…”

Section: Simulation Resultsmentioning

confidence: 99%

“…At the end of this section, some of the main advantages of the proposed neural network are summarized below. In comparison with conventional numerical methods, in designing new neural network, a properly derived dynamical equation can ensure that the equilibrium point of the neural network corresponds to the optimal solution of the optimization problem under study. Compared with other existing neural networks for NCNO problem, for instance, models in Xia et al () and Effati and Moghaddas (), the proposed neural network has several merits. First, the proposed model can be convergent to an exact solution of NCNO problem .…”

Section: Simulation Resultsmentioning

confidence: 99%

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An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

Moghaddas

Tohidi

2019

Expert Systems

Self Cite

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This paper presents a recurrent neural network for solving nonconvex nonlinear optimization problems subject to nonlinear inequality constraints. First, the p‐power transformation is exploited for local convexification of the Lagrangian function in nonconvex nonlinear optimization problem. Next, the proposed neural network is constructed based on the Karush–Kuhn–Tucker (KKT) optimality conditions and the projection function. An important property of this neural network is that its equilibrium point corresponds to the optimal solution of the original problem. By utilizing an appropriate Lyapunov function, it is shown that the proposed neural network is stable in the sense of Lyapunov and convergent to the global optimal solution of the original problem. Also, the sensitivity of the convergence is analysed by changing the scaling factors. Compared with other existing neural networks for such problem, the proposed neural network has more advantages such as high accuracy of the obtained solutions, fast convergence, and low complexity. Finally, simulation results are provided to show the benefits of the proposed model, which compare to or outperform existing models.

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Section: Simulation Resultsmentioning

confidence: 88%

Section: Simulation Resultsmentioning

confidence: 89%

\frac{d}{d t} ((), \begin{matrix} center \\ array x (t) \\ array μ (t) \end{matrix}) = s ([], \begin{matrix} array - x + {(x)}^{+} - \nabla f ({(x)}^{+}) - \nabla g ({(x)}^{+}) {(μ)}^{+} \\ array - μ + {(μ)}^{+} + (g ({(x)}^{+}) - b) \end{matrix}),

where ( x ) + =( x 1 + ,…, x n + ) T , ( μ ) + =( μ 1 + ,…, μ m + ) T ,

{x_{i}}^{+} = \max ({}, 0, x_{i})

{μ_{i}}^{+} = \max ({}, 0, μ_{i})

, and s >0 is a designing constant.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…Xia et al introduced the following dynamic system for solving NCNO problem :

\frac{d}{d t} ((), \begin{matrix} center \\ array x (t) \\ array μ (t) \end{matrix}) = s ([], \begin{matrix} array - x + {(x)}^{+} - \nabla f ({(x)}^{+}) - \nabla g ({(x)}^{+}) {(μ)}^{+} \\ array - μ + {(μ)}^{+} + (g ({(x)}^{+}) - b) \end{matrix}),

where ( x ) + =( x 1 + ,…, x n + ) T , ( μ ) + =( μ 1 + ,…, μ m + ) T ,

{x_{i}}^{+} = \max ({}, 0, x_{i})

{μ_{i}}^{+} = \max ({}, 0, μ_{i})

, and s >0 is a designing constant. In addition, we consider a gradient‐based neural network model (Effati & Moghaddas, ) for solving whose state variable is given by the following dynamic system:

\frac{d w false(t false)}{d t} = - κ \nabla ((), \frac{1}{2} {(‖‖, normalΦ false(w false))}^{2}), w false(t_{0} false) = w_{0},

where

w = ((), x, μ_{p}) \in X \times {double-struckR}_{+}^{m}

normalΦ false(x, μ_{p} false) = false({false(\nabla_{x} L_{p} false(x, μ_{p} false) false)}^{T}, false(scriptZ false(x, μ_{p} f...

…”

Section: Simulation Resultsmentioning

confidence: 99%

Section: Simulation Resultsmentioning

confidence: 99%

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An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

Moghaddas

Tohidi

2019

Expert Systems

Self Cite

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A Neurodynamic Model to Solve Nonlinear Pseudo-Monotone Projection Equation and Its Applications

Eshaghnezhad

Effati

Mansoori

2017

IEEE Trans. Cybern.

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In this paper, a neurodynamic model is given to solve nonlinear pseudo-monotone projection equation. Under pseudo-monotonicity condition and Lipschitz continuous condition, the projection neurodynamic model is proved to be stable in the sense of Lyapunov, globally convergent, globally asymptotically stable, and globally exponentially stable. Also, we show that, our new neurodynamic model is effective to solve the nonconvex optimization problems. Moreover, since monotonicity is a special case of pseudo-monotonicity and also since a co-coercive mapping is Lipschitz continuous and monotone, and a strongly pseudo-monotone mapping is pseudo-monotone, the neurodynamic model can be applied to solve a broader classes of constrained optimization problems related to variational inequalities, pseudo-convex optimization problem, linear and nonlinear complementarity problems, and linear and convex quadratic programming problems. Finally, several illustrative examples are stated to demonstrate the effectiveness and efficiency of our new neurodynamic model.

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Solving Multiextremal Problems by Using Recurrent Neural Networks

Malek

Hosseinipour-Mahani

2018

IEEE Trans. Neural Netw. Learning Syst.

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In this paper, a neural network model for solving a class of multiextremal smooth nonconvex constrained optimization problems is proposed. Neural network is designed in such a way that its equilibrium points coincide with the local and global optimal solutions of the corresponding optimization problem. Based on the suitable underestimators for the Lagrangian of the problem, one give geometric criteria for an equilibrium point to be a global minimizer of multiextremal constrained optimization problem with or without bounds on the variables. Both necessary and sufficient global optimality conditions for a class of multiextremal constrained optimization problems are presented to determine a global optimal solution. By study of the resulting dynamic system, it is shown that under given assumptions, steady states of the dynamic system are stable and trajectories of the proposed model converge to the local and global optimal solutions of the problem. Numerical results are given and related graphs are depicted to illustrate the global convergence and performance of the solver for multiextremal constrained optimization problems.

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A novel neural network based on NCP function for solving constrained nonconvex optimization problems

Cited by 4 publications

References 57 publications

An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

A Neurodynamic Model to Solve Nonlinear Pseudo-Monotone Projection Equation and Its Applications

Solving Multiextremal Problems by Using Recurrent Neural Networks

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