A Novel Neural Network for Solving Singular Nonlinear Convex Optimization Problems

Liu, Lijun; Ge, Rendong; Gao, Pengyuan

doi:10.1007/978-3-642-24958-7_64

Cited by 2 publications

(1 citation statement)

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“…Due to the inherent Parallel mechanism and highspeed of hardware implementations, efforts to tackle such problems by using neural systems are promising and creative. Attempt was made for the first time in our recent paper [18] to solve unconstraint singular optimization problem, which turned out to be feasible and effecttive. In this paper, we further improve such result to the case of singular optimization problem with bounded variables constraint.…”

Section: Introductionmentioning

confidence: 99%

Neural Network Approach for Solving Singular Convex Optimization with Bounded Variables

Ge¹,

Liu²,

Xu³

2013

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Although frequently encountered in many practical applications, singular nonlinear optimization has been always recognized as a difficult problem. In the last decades, classical numerical techniques have been proposed to deal with the singular problem. However, the issue of numerical instability and high computational complexity has not found a satisfactory solution so far. In this paper, we consider the singular optimization problem with bounded variables constraint rather than the common unconstraint model. A novel neural network model was proposed for solving the problem of singular convex optimization with bounded variables. Under the assumption of rank one defect, the original difficult problem is transformed into nonsingular constrained optimization problem by enforcing a tensor term. By using the augmented Lagrangian method and the projection technique, it is proven that the proposed continuous model is convergent to the solution of the singular optimization problem. Numerical simulation further confirmed the effectiveness of the proposed neural network approach.

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Section: Introductionmentioning

confidence: 99%