Nonlinear programming without computation

Chua, Leon O.; Lin, G. N.

doi:10.1109/tcs.1984.1085482

Cited by 194 publications

(93 citation statements)

References 9 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%

“…A transimpedance integrator provides a convenient method of realizing the term as the input to the dynamic element that computes the state variable If an ideal transconductor is used in conjunction with a capacitor a lossy integrator with finite time constant results. The ideal weighted solution for (1), in a small signal sense, is given by (14) with the proviso that remains within the linear range of the integrator (which is typically a few tens of millivolts). Fig.…”

Section: G Voltage Mode Dynamic Operator Implementationmentioning

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%

Section: G Voltage Mode Dynamic Operator Implementationmentioning

confidence: 99%

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

Soumyanath

Borkar

1999

IEEE Trans. Circuits Syst. I

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“…showed that the Tank and Hopfield linear programming networ:k is a specific implementation of the canonical nonlinear programming circuit of Chua and Lin ( [5]) with a capacitor added to account for the dynamic behavior of the circuit. Kennedy and Chua ([9]) examined the stability of the modified canonical nonlinear programming circuit and proposed a neural network circuit implementation which could be utilized to solve a class of nonlinear programming prloblems.…”

Section: And Chua ([8])mentioning

confidence: 99%

“…Other canonical circuits were later introduced by Huertas, Rueda, Rodriguez-Vazquez and Chua ([4]). In [5], Chua and Lirl presented a circuit implementation which is capable of solving various progra,mming problerns without numerical computation. Later, Wilson ([6]) stressed the importance of negative components in quadratic programming and proposed an im.plementation which utilized floating negative resistors.…”

Section: Introductionmentioning

confidence: 99%

On Solving Constrained Optimization Problems with Neural Networks: A Penalty Function Method Approach

Lillo

Hul

Loh

et al. 1992

1992 American Control Conference

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This paper is concerned with utilizing analog circuits to solve various linear and nonlinear programming problems. The dynamics of these circuits are analyzed. Then, the previously proposed circuit implementations for solving optimization problems are examined. A new nonlinear programming network and its circuit implementation is then introduced which utilizes the nonlinearities to eliminate the problems encountered in previous circuit implementations.

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“…The ANNs are used to solve complex problems and to obtain solution of constrained optimization problems [19]. The canonical nonlinear programming circuit was developed by Chua and Lin [20]. In literature, ANNs are used in signal processing areas such as one [21] and two dimensional [22] filter design and image processing [23].…”

Section: Introductionmentioning

confidence: 99%

The Using of ANN at Design of Window Function Having Useful Spectral Parameters

KAYA

2016

Fifth International Conference on Advances in Computing, Electronics and Electrical Technology - CEET 2016

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Abstract-The window functions are proposed structures at many application areas. The windows with helping two or more independent parameters show useful spectral characteristic. Kaiser window has been used at many areas because of the fact that it has good characteristic specification such as mainlobe width and the ripple ratio for various applications but Kaiser window having two parameters cannot control the sidelobe roll-off ratio. The ultraspherical window having three independent parameters has better sidelobe rolloff ratio than other windows in literature. At work, the coefficients of a new window function that has side-lobe roll-off ratio characteristic of ultraspherical window and Kaiser window's main-lobe width and ripple ratio were obtained by helping of artificial neural networks (ANN). 3000 data are used for training and testing of ANN. Sixty-five percentage of these data was used for learning of ANN and thirty-five percentage of that was used for testing process. It was observed that between the desired values and the obtained values using ANN were good agreements. Hence, a new window having better mainlobe width ripple ratio and side lobe roll-off ratio than other windows in spectral parameters at literature was modeled with ANN.

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Nonlinear programming without computation

Cited by 194 publications

References 9 publications

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

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

On Solving Constrained Optimization Problems with Neural Networks: A Penalty Function Method Approach

The Using of ANN at Design of Window Function Having Useful Spectral Parameters

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