Exponential stability and a systematic synthesis of a neural network for quadratic minimization

Sudharsanan, Subramania I.; Sundareshan, Malur K.

doi:10.1016/0893-6080(91)90014-v

Cited by 99 publications

(51 citation statements)

References 15 publications

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“…An important instance here is the gradient-descent algorithm (7) which reduces to (3) for (8) For quadratic , say, with is a two-contraction if Note that we do not change the gradient-descent algorithm; only the view point. Hence, the system is equivalent to those reported in [2], [7], [14], and [30] for quadratic programming. Fig.…”

Section: B Nonlinear Programmingmentioning

confidence: 99%

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An analog scheme for fixed-point computation-Part II: Applications

Soumyanath

Borkar

1999

IEEE Trans. Circuits Syst. I

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Abstract-In a companion paper [6] we presented theoretical analysis of an analog network for fixed-point computation. This paper applies these results to several applications from numerical analysis and combinatorial optimization, in particular: 1) solving systems of linear equations; 2) nonlinear programming; 3) dynamic programing; and 4) network flow computations. Schematic circuits are proposed for representative cases and implementation issues are discussed. Exponential convergence is established for a fixed-point computation that determines the stationary probability vector for a Markov chain. A fixedpoint formulation of the single source shortest path problem (SPP) that will always converge to the exact shortest path is described. A proposed implementation, on a 2-complementary metal-oxide-semiconductor (CMOS) process, for a fully connected eight-node network is described in detail. The accuracy and settling time issues associated with the proposed design approach are presented.

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Section: B Nonlinear Programmingmentioning

confidence: 99%

“…[33]. The work by Sudarshanan and Sunderasan [30] and its improvements [7] describe an analog parallel technique for quadratic optimization. An analog network for solving systems of linear equations is also discussed in [17].…”

Section: Introductionmentioning

confidence: 99%

An analog scheme for fixed-point computation-Part II: Applications

Soumyanath

Borkar

1999

IEEE Trans. Circuits Syst. I

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“…Since the exponential convergence rate could be used to determine the speed of neural computation, it is interesting to study the estimate of exponential convergence rate and exponential stability of neural networks. Some results on the exponential stability of neural networks could be found in [1], [8], and [10]. In this paper we shall study the estimation of exponential convergence rate and the exponential stability of (1).…”

Section: It Is Easy To See That If Is Locally Lipschitz Thenmentioning

confidence: 99%

Estimate of exponential convergence rate and exponential stability for neural networks

Zhang

Heng

1999

IEEE Trans. Neural Netw.

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Abstract-Estimate of exponential convergence rate and exponential stability are studied for a class of neural networks which includes the Hopfield neural networks and the cellular neural networks. Both local and global exponential convergence is discussed. Theorems for estimate of exponential convergence rate are established and the bounds on the rate of convergence are given. The domains of attraction in the case of local exponential convergence are obtained. Simple conditions are presented for checking exponential stability of the neural networks.Index Terms-Convergence rate, neural networks, stability.

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“…where (18) The solution set of F(x, y, z) = 0 is just the equilibrium point set of dynamic system (5). In Theorem 2, we will give the relationship between the solution set of model (4) and the equilibrium point set of dynamic system (5).…”

Section: Proof: See [11]mentioning

confidence: 99%

Constrained Least Absolute Deviation Neural Networks

Wang

Peterson

2008

IEEE Trans. Neural Netw.

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It is well known that least absolute deviation (LAD) criterion or L 1 -norm used for estimation of parameters is characterized by robustness, i.e., the estimated parameters are totally resistant (insensitive) to large changes in the sampled data. This is an extremely useful feature, especially, when the sampled data are known to be contaminated by occasionally occurring outliers or by spiky noise. In our previous works, we have proposed the least absolute deviation neural network (LADNN) to solve unconstrained LAD problems. The theoretical proofs and numerical simulations have shown that the LADNN is Lyapunov-stable and it can globally converge to the exact solution to a given unconstrained LAD problem. We have also demonstrated its excellent application value in timedelay estimation. More generally, a practical LAD application problem may contain some linear constraints, such as a set of equalities and/or inequalities, which is called constrained LAD problem, whereas the unconstrained LAD can be considered as a special form of the constrained LAD. In this paper, we present a new neural network called constrained least absolute deviation neural network (CLADNN) to solve general constrained LAD problems. Theoretical proofs and numerical simulations demonstrate that the proposed CLADNN is Lyapunov stable and globally converges to the exact solution to a given constrained LAD problem, independent of initial values. The numerical simulations have also illustrated that the proposed CLADNN can be used to robustly estimate parameters for nonlinear curve fitting, which is extensively used in signal and image processing.

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Exponential stability and a systematic synthesis of a neural network for quadratic minimization

Cited by 99 publications

References 15 publications

An analog scheme for fixed-point computation-Part II: Applications

An analog scheme for fixed-point computation-Part II: Applications

Estimate of exponential convergence rate and exponential stability for neural networks

Constrained Least Absolute Deviation Neural Networks

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