Projection Neural Network Research Articles

A system of fractional-order interval projection neural networks

In this paper, a system of fractional-order interval projection neural networks is introduced and investigated. Under some suitable assumptions, the existence and uniqueness of the equilibrium point of this type of interval projection neural networks is proved. Moreover, α-exponential stability of this type of neural networks is obtained. Also, in the last section, we give two numerical examples to demonstrate the validity of our results.

A Complex-Valued Projection Neural Network for Constrained Optimization of Real Functions in Complex Variables.

In this paper, we present a complex-valued projection neural network for solving constrained convex optimization problems of real functions with complex variables, as an extension of real-valued projection neural networks. Theoretically, by developing results on complex-valued optimization techniques, we prove that the complex-valued projection neural network is globally stable and convergent to the optimal solution. Obtained results are completely established in the complex domain and thus significantly generalize existing results of the real-valued projection neural networks. Numerical simulations are presented to confirm the obtained results and effectiveness of the proposed complex-valued projection neural network.

A new delayed projection neural network for solving quadratic programming problems with equality and inequality constraints

In this paper, a new delayed projection neural network is presented for solving quadratic programming problems subject to equality and inequality constraints. Compared with the existing neural networks for solving such problems, the proposed neural network has fewer neurons and a one-layer architecture. Further, we demonstrate the existence and uniqueness of the continuous solution. By using differential inequality technique, the new neural network is shown to be globally exponentially convergent to optimal solution. Finally, recurring to the numerical method, simulation results with some applications show the effectiveness of the proposed neural network.

An efficient projection neural network for solving bilinear programming problems

In this paper the application of projection neural network for solving bilinear programming problems (BLPs) is obtained. So far as we know, no study has yet been attempted for these problems via neural network. In fact, some interesting reformulations of BLP and mixed-integer bilinear programming problem (MIBLP) with a binary vector to linear complementarity problem (LCP) are given. Additionally, we show that the special type of MIBLP with a binary vector is equal to a quadratic program and on the other hand, it is equal to a mixed-integer linear program (MILP). Finally, we use a neural network to solve projection equation which has the same solution with LCP. Then, by presenting a Lyapunov function, we show that the proposed neural network is globally asymptotically stable. Illustrative examples are given to show the effectiveness and efficiency of our method.

A Projection Neural Network for Constrained Quadratic Minimax Optimization.

This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

One-Layer Continuous-and Discrete-Time Projection Neural Networks for Solving Variational Inequalities and Related Optimization Problems

This paper presents one-layer projection neural networks based on projection operators for solving constrained variational inequalities and related optimization problems. Sufficient conditions for global convergence of the proposed neural networks are provided based on Lyapunov stability. Compared with the existing neural networks for variational inequalities and optimization, the proposed neural networks have lower model complexities. In addition, some improved criteria for global convergence are given. Compared with our previous work, a design parameter has been added in the projection neural network models, and it results in some improved performance. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural networks.

A collective neurodynamic optimization approach to bound-constrained nonconvex optimization

This paper presents a novel collective neurodynamic optimization method for solving nonconvex optimization problems with bound constraints. First, it is proved that a one-layer projection neural network has a property that its equilibria are in one-to-one correspondence with the Karush–Kuhn–Tucker points of the constrained optimization problem. Next, a collective neurodynamic optimization approach is developed by utilizing a group of recurrent neural networks in framework of particle swarm optimization by emulating the paradigm of brainstorming. Each recurrent neural network carries out precise constrained local search according to its own neurodynamic equations. By iteratively improving the solution quality of each recurrent neural network using the information of locally best known solution and globally best known solution, the group can obtain the global optimal solution to a nonconvex optimization problem. The advantages of the proposed collective neurodynamic optimization approach over evolutionary approaches lie in its constraint handling ability and real-time computational efficiency. The effectiveness and characteristics of the proposed approach are illustrated by using many multimodal benchmark functions.

Neural network for nonsmooth pseudoconvex optimization with general constraints

In this paper, a one-layer recurrent projection neural network is proposed for solving pseudoconvex optimization problems with general convex constraints. The proposed network in this paper deals with the constraints into two parts, which brings the network simpler structure and better properties. By the Tikhonov-like regularization method, the proposed network need not estimate the exact penalty parameter in advance. Moreover, comparing with some existing neural networks, the proposed network can solve more general constrained pseudoconvex optimization problems. When the solution of the proposed network is bounded, it converges to the optimal solution set of considered optimization problem, which may be nonsmooth and nonconvex. Meantime, some sufficient conditions are presented to guarantee the boundedness of the solution of the proposed network. Numerical examples with simulation results are given to illustrate the effectiveness and good characteristics of the proposed network for solving constrained pseudoconvex optimization.

Application of Neural Network in Duration Implicit Cost Control for Construction Projects

According to the characteristics of construction project, it set the third level of duration implicit cost, deepening the understanding of the duration implicit cost in construction project. Through analyzing the similar characteristics of the technique of project network diagram and neural network, it built a duration implicit cost control model based on neural network, which can adjust the project network diagram to the optimization direction. Aiming at the defects of the traditional neural network, the variable learning rate back-propagation arithmetic and the additional momentum method were introduced, and the duration implicit cost control model was built, improving the accuracy of the control for the neural network technique.

A one-layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints.

This paper presents a one-layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints. The proposed neural network is designed based on two projection operators: linear equality constraints, and bound constraints. The objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex (pseudoconvex) on a set defined by the constraints. Compared with existing recurrent neural networks for nonsmooth optimization, the proposed model does not have any design parameter, which is more convenient for design and implementation. It is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex. Simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

A projection neural network with mixed delays for solving linear variational inequality

This paper presents a projection neural network with discrete delays and distributed delays (i.e. mixed delays) for solving linear variational inequality (LVI). By the Lyapunov theory and the linear matrix inequality (LMI) approach, the neural network is proved to be globally exponentially convergent to the solution of LVI. Compared with existing neural networks for solving LVI, the proposed one features the ability of solving a class of non-monotone LVI. One numerical example is provided to illustrate the effectiveness and the satisfactory performance of the neural network.

A new delayed projection neural network for solving quadratic programming problems subject to linear constraints

In this paper, a new projection neural network with two time delays is proposed for solving quadratic programming problems subject to linear constraints. And we give the existence of the continuous solution. By the theory of functional differential equation, the proposed neural network is proved to be globally exponentially stable under some conditions. Simulation results with some applications show the performance and characteristic of the proposed neural network.

Research on the related problems of extended alternating projection neural network

The paper studies several related problems of the Extended Alternating Projection Neural Network (EAPNN). Firstly the mathematical relation between the interconnection matrix and the library pattern matrix, and the stability of the EAPNN with infinite precision data have been studied, strictly mathematical proofs for them have been given. After analyzing the finite precision influence on the training method of the EAPNN, the paper proposes an improved training method for the EAPNN with finite precision data and gives a practical threshold-value determination method. Then the mathematical relation among the factors influencing the association times has been studied and the mathematical expression of the association times for reaching the expected association precision, while network being used for CAM, has been deduced. Finally simulation experiments have been designed and simulation results demonstrate the validity of theoretical analyses.

New results for neutral-type delayed projection neural network to solve linear variational inequalities

Recently, a neutral-type delayed projection neural network (NDPNN) was developed for solving variational inequality problems. This paper addresses the global stability and convergence of the NDPNN and presents new results for it to solve linear variational inequality (LVI). Compared with existing convergence results for neural networks to solve LVI, our results do not require the LVI that is monotone so as to guarantee the NDPNN that can solve a class of non-monotone LVI. All the results are expressed in terms of linear matrix inequalities, which can be easily checked. Simulation examples demonstrate the effectiveness of the obtained results.

Analysis of the contour structural irregularity of skin lesions using wavelet decomposition

The boundary irregularity of skin lesions is of clinical significance for the early detection of malignant melanomas and to distinguish them from other lesions such as benign moles. The structural components of the contour are of particular importance. To extract the structure from the contour, wavelet decomposition was used as these components tend to locate in the lower frequency sub-bands. Lesion contours were modeled as signatures with scale normalization to give position and frequency resolution invariance. Energy distributions among different wavelet sub-bands were then analyzed to extract those with significant levels and differences to enable maximum discrimination.Based on the coefficients in the significant sub-bands, structural components from the original contours were modeled, and a set of statistical and geometric irregularity descriptors researched that were applied at each of the significant sub-bands. The effectiveness of the descriptors was measured using the Hausdorff distance between sets of data from melanoma and mole contours. The best descriptor outputs were input to a back projection neural network to construct a combined classifier system. Experimental results showed that thirteen features from four sub-bands produced the best discrimination between sets of melanomas and moles, and that a small training set of nine melanomas and nine moles was optimum.

A new result for projection neural networks to solve linear variational inequalities and related optimization problems

In recent years, a projection neural network was proposed for solving linear variational inequality (LVI) problems and related optimization problems, which required the monotonicity of LVI to guarantee its convergence to the optimal solution. In this paper, we present a new result on the global exponential convergence of the projection neural network. Unlike existing convergence results for the projection neural network, our main result does not assume the monotonicity of LVI problems. Therefore, the projection neural network can be further guaranteed to solve a class of non-monotone LVI and non-convex optimization problems. Numerical examples illustrate the effectiveness of the obtained result.

Efficient neural networks for solving variational inequalities

In this paper, we propose efficient neural network models for solving a class of variational inequality problems. Our first model can be viewed as a generalization of the basic projection neural network proposed by Friesz et al. [3]. As the basic projection neural network, it only needs some function evaluations and projections onto the constraint set, which makes the model very easy to implement, especially when the constraint set has some special structure such as a box, or a ball. Under the condition that the underlying mapping F is pseudo-monotone with respect to a solution, a condition that is much weaker than those required by the basic projection neural network, we prove the global convergence of the proposed neural network. If F is strongly pseudo-monotone, we prove its globally exponential stability. Then to improve the efficient of the neural network, we modify it by choosing a new direction that is bounded away from zero. Under the condition that the underlying mapping F is co-coercive, a condition that is a little stronger than pseudo-monotone but is still weaker than those required by the basic projection neural network, we prove the exponential stability and global convergence of the improved model. We also reported some computational results, which illustrated that the new method is more efficient than that of Friesz et al. [3].

A one-layer recurrent neural network for constrained pseudoconvex optimization and its application for dynamic portfolio optimization

In this paper, a one-layer recurrent neural network is proposed for solving pseudoconvex optimization problems subject to linear equality and bound constraints. Compared with the existing neural networks for optimization (e.g., the projection neural networks), the proposed neural network is capable of solving more general pseudoconvex optimization problems with equality and bound constraints. Moreover, it is capable of solving constrained fractional programming problems as a special case. The convergence of the state variables of the proposed neural network to achieve solution optimality is guaranteed as long as the designed parameters in the model are larger than the derived lower bounds. Numerical examples with simulation results illustrate the effectiveness and characteristics of the proposed neural network. In addition, an application for dynamic portfolio optimization is discussed.

Solving Interval Quadratic Program with Box Set Constraints in Engineering by a Projection Neural Network

Solving Interval Quadratic Program with Box Set Constraints in Engineering by a Projection Neural Network

Efficient recurrent neural network model for the solution of general nonlinear optimization problems

In this paper, we propose a projection neural network model for solving nonlinear convex optimization problems with general linear constraints. Compared with the existing neural network models for solving nonlinear optimization problems, the proposed neural network can be applied to solve a broad class of constrained optimization problems such as degenerate, saddle point, and quadratic problems. It is shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent. This model is exponentially stable. Simulation results are given to illustrate the global convergence and performance of the proposed model for various classes of constrained optimization problems. Both theoretical and numerical approaches are considered. Numerical results are in good agreement with the proved theoretical concepts.