Titlebook: Neural Networks in Optimization; Xiang-Sun Zhang Book 2000 Springer Science+Business Media Dordrecht 2000 Mathematica.Optimization Theory.

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A Review on NN for Continuious Optimizationimization problems and optimization problems with continuous variables. Since then a variety of NN models have been proposed to solve linear programming (LP) problems and quadratic programming (QP) problems. This is because that LP and QP have fundamental importance in the theory and practice of opt

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Preliminariesor {.}., . = 1, ? , .. The entry in row i and column . of a matrix . is denoted by ... .(.)is a column vector-valued function with scalar-valued functions ..(.), ..(.), ... ,.. (.) as its components. In the following chapters, we sometimes write ..,.. as abbreviations for . (..),.(..).

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Introduction to Mathematical Programmingn from positive to negative, splitting a variable without bound into two positively bounded variables, etc. The readers can find these techniques in almost all books about linear programming (to mention a few, [71], [94], [105], [117], [205])

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Feedback Neural Networksent is fed back to the various layers from the output layer to reduce the overall output error with regard to the known input-output experience. When the training stage ends, the feedback interaction within the network no longer remains.

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A Review on NN for Continuious Optimizationimization. There were also a few models for general nonlinear programming (NP) problem. All of these networks are feedback continuous networks similar to the Hopfield network.It is expected that there will be more models emerging.

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Algorithms for Unconstrained Nonlinear Programming, Murray and Wright [123], and Luenberger [205]). In this section we only introduce some basic algorithms which have already been frequently used or would be used in the future in artificial neural network study. The same consideration will be taken when we arrange the materials for the other chapters.

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