Nonlinear Optimization Models and Solving Algorithms based on Appropriate Neural Networks

This work contains a complete set of algorithms for several quadratic and nonlinear optimization problems. The problem constraints are very differently. For each type of constraint an appropriate algorithm is given. The algorithms for linear bound constraints and nonlinear optimization are based on neural networks and uses a system of differential equations. In order to reduce the sensitivity and round off errors a preconditioning method is used. A great number of numerical applications illustrates the algorithms. We use the square matrices M of the type n x n or rectangular matrices M of type m x n. All the used vectors are column vectors i.e. x, c, d, p, r, u, V, W and denote, for example, x = x(nx1) or x epsilon R-n, x = (x(i)). The letter T means the transposition. Here we enumerate several nonlinear optimization models and mention the appropriate algorithms to solve them. There are a lot of quadratic optimization (QO) models (or quadratic programming (QP) models) and nonlinear optimization models (NO) and here we mention several of them. We denote by theta the null vector of an appropriate space, let us say R-n and x epsilon R-n is the unknown vector of the any optimization problem.