In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given. [ABSTRACT FROM AUTHOR]
In this paper, an iterative method is presented for finding the bisymmetric solutions of a pair of consistent matrix equations A1XB1=C1, A2XB2=C2, by which a bisymmetric solution can be obtained in finite iteration steps in the absence of round-off errors. Moreover, the solution with least Frobenius norm can be obtained by choosing a special kind of initial matrix. In the solution set of the matrix equations, the optimal approximation bisymmetric solution to a given matrix can also be derived by this iterative method. The efficiency of the proposed algorithm is shown by some numerical examples. [ABSTRACT FROM AUTHOR]
The development of optimization theory originated with economic requirements and problems, where optimal strategy was to be determined mathematically. At about the same time, approximation theory, which was already well developed, experienced a reinvigoration brought about by the advent of electronic computers. In this paper, what follows, we recall the functional analysis that constitutes the framework of our development of an extended conjugate gradient algorithm that does not involve any approximation in any of its steps. This is a computational enhancement over the conventional conjugate gradient method which is dependent on some approximation theory. We use this improved algorithm for the construction of some functional inequalities. [ABSTRACT FROM AUTHOR]