On the Problem of Local Minima in Backpropagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Neural Networks: A Comprehensive Foundation
Neural Networks: A Comprehensive Foundation
Fast curvature matrix-vector products for second-order gradient descent
Neural Computation
Bio-inspired and gradient-based algorithms to train MLPs: The influence of diversity
Information Sciences: an International Journal
Newton's Method for Multiobjective Optimization
SIAM Journal on Optimization
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In an extension of previous work, here we introduce a second-order optimization method for determining optimal paths from the substrate to a target product of a metabolic network, through which the amount of the target is maximum. An objective function for the said purpose, along with certain linear constraints, is considered and minimized. The basis vectors spanning the null space of the stoichiometric matrix, depicting the metabolic network, are computed, and their convex combinations satisfying the constraints are considered as flux vectors. A set of other constraints, incorporating weighting coefficients corresponding to the enzymes in the pathway, are considered. These weighting coefficients appear in the objective function to be minimized. During minimization, the values of these weighting coefficients are estimated and learned. These values, on minimization, represent an optimal pathway, depicting optimal enzyme concentrations, leading to overproduction of the target. The results on various networks demonstrate the usefulness of the methodology in the domain of metabolic engineering. A comparison with the standard gradient descent and the extreme pathway analysis technique is also performed. Unlike the gradient descent method, the present method, being independent of the learning parameter, exhibits improved results.