Based On The Neural Network Method To Solve Inverse Optimal Value Problem

Inverse optimal value problem is used extensively in geophysical sciences andmedical imaging, traffic equilibrium, railroad scheduling, portfolio optimization, isotonicregression, stability analysis etc. It should be note that, in the references above, almost allresults focused mainly on the study of the classical numerical algorithm for the inverseoptimal value problem. However, in lots of engineering applications, many optimizationproblems need to be solved in real time. When the problem is very complex, use thetraditional optimization algorithm may need a long calculation time, even sometimes thecomputing time is what we are not acceptable. Compared with classical optimizationapproaches, the appearance of neural computing approach satisfies the demand ofreal-time optimal solutions. The main advantage of neural network method is that thedynamic solution process is essentially a parallel and distributed, which can make thespeed of calculation greatly improved. This paper studies the application of the neuralnetworks to solve inverse optimization. The full text is divided into five chapters:The first chapter presents the neural network development and general situation ofresearch, and analysis the neural network methods for solving optimization problem inpresent situation.The second chapter presents the required basic knowledge and the basic principle ofthe optimization, and presents some definitions and lemmas for the stability analysis of theneural network.The third chapter studies the application of nonlinear neural network in solving theinverse optimal value problem with linear constraints. And analyzed the existence anduniqueness of the equilibrium point, and the globally asymptotic stability of the nonlinearneural network.The forth chapter studies the application of nonlinear neural network in solving theinverse optimal value problem with convex constraints. And analyzed the existence anduniqueness of the equilibrium point, and the globally asymptotic stability of the nonlinearneural network.The fifth chapter of the paper applied nonlinear neural network to solve two inverse optimization problems with practical background.