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Feasibility and Effectiveness Analysis of Optimization Problems Solving Using Generalized Hopfield Networks

Student: Mariya Polischuk

Supervisor: Efim Pelinovsky

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Business Informatics (Bachelor)

Year of Graduation: 2019

One of the most important criteria for solving optimization problems is the time to find a solution. It is known that Hopfield neural networks successfully cope with the solution of optimization problems with a quadratic activation function. But there are more complex tasks, the objective function of it is compounded and complicated by many limitations in the domain of definition. Networks that may get a solution to such problems successfully are called Generalized Hopfield networks. The work is an attempt to analyze and summarize the ability of Hopfield neural networks to cope with non-quadratic objective functions. The paper considers discrete nonlinear optimization problems with constraints, and applies optimization algorithms Augmented Lagrangian and Successive Quadratic Programming to them. The equations of motion are described by the methods of Cauchy and Newton. The implementation and testing of neural networks implemented in Python with using libraries of parallel computations.

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