Neural networks for nonlinear programming

By Michael Peter Kennedy, Leon Ong Chua. 1988

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Citations in the corpus

OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, background): “Indeed, the general idea of solving restricted classes of optimization problem using neural networks goes back many decades (Kennedy & Chua, 1988; Lillo et al., 1993), but has seen a number of advances in recent years.”
IEEE Transactions on Neural Networks (2008, background): “Kennedy and Chua [5] recast the canonical circuit in a neural network framework and prove the stability.”
A Second-Order Multi-Agent Network for Bound-Constrained Distributed Optimization (2015, background): “Kennedy and Chua [16] developed a recurrent neural network for nonlinear optimization.”
A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks (2014, background): “Another important example concerns the class of neural networks introduced in [131] to solve linear and nonlinear programming TABLE I COMPARISONS OF DIFFERENT TYPES OF ACTIVATION FUNCTIONS problems, in which the constraint neurons are with a diode-like input–output activations.”
A projection neural network and its application to constrained optimization problems (2002, background): “Although the equilibrium point of the Tank and Hopfield network may not be a solution of the original problem, this seminal work has inspired many researchers to investigate other neural networks for solving linear and nonlinear programming problems (see [13]–[28] and therein Refs.”
Trajectory-Tracking Control of Mobile Robot Systems Incorporating Neural-Dynamic Optimized Model Predictive Approach (2016, background): “by analog circuits could be much simpler than those of the existing recurrent neural network methods [39], [40].”
Global convergence of neural networks with discontinuous neuron activations (2003, background): “Another important example concerns the class of neural networks introduced by Kennedy and Chua [4] to solve linear and nonlinear programming problems.”
Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain (2005, background): “One particularly interesting case corresponds to the networks for linear and quadratic programming problems introduced in [22], where the constraint neurons are diode-like exponential nonlinearities, or unbounded piecewise linear functions approximating the exponential.”