A Neural Network-Type Cutting Plane Algorithm for Nonsmooth Constrained Optimization

For nonsmooth constrained optimization, we propose a new method for solving subproblems of cutting plane algorithm by employing the idea of recurrent neural network. The recurrent neural network is described by differential inclusions which is involved with the subdifferential of the model function. Since the subdifferential of the model function with simple structure is easy to compute which makes the presented algorithm easier to implement. Compared with the classical cutting plane method, our method provides an alternative way to solve subproblems which decreases the computational complexity, and at the same time the proposed method avoids the accumulation of information of iterative points which increases the stability of the method by introducing the aggregation technique. The sequence of model function at the limit points of solution trajectories obtained by solving recurrent neural network converges to the optimal value of original nonsmooth constrained optimization. Finally, four examples are given to testify the efficiency and validity of the proposed method.