A Neural Network Algorithm Based on Penalty Function Method for Solving Non-smooth Pseudoconvex Optimization Problems and Its Applications
To address the nonsmooth pseudoconvex optimization problems encountered in practical applications,an innovative solution is proposed:a single-layer neural network algorithm that integrates the concept of penalty functions and the theory of differential inclusions.Firstly,through mathematical theory,it is proved that this algorithm can ensure that the state solutions ultimately converge to the optimal solution of the pseudoconvex optimization problem,thus establishing the correctness of the proposed algorithm.Secondly,the effectiveness of the algorithm is further verified through the analysis of simulated convergence results from two numerical experiments.Finally,the applications of this algorithm to practical problems demonstrate its practical application value in solving pseudoconvex optimization issues.Compared with existing neural network algorithms,this algorithm can not only solve more general pseudoconvex optimization problems with convex inequality and equality constraints but also tackle practical application issues.Moreover,the algorithm has a simple hierarchical structure,does not require the calculation of precise penalty parameters,allows for the selection of any starting point,and does not add any auxiliary variable,which thus provides an effective approach to solving pseudoconvex optimization problems.
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