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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]

We propose a quasi-Newton line-search method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its practical behaviour. Our extensive computational study shows the potential of the proposed method from different angles, such as its performance compared with some other existing packages, the profile of its computations, and its large-scale adaptation. We then conclude the paper with the convergence analysis of the proposed method. [ABSTRACT FROM AUTHOR]

An optimal control problem governed by the first bi-harmonic equation with the integral constraint for the state and its spectral approximations based on a mixed formulation are investigated. The optimality conditions of the exact and the discrete optimal control systems are derived. The a priori error estimates of high order spectral accuracy are obtained. Furthermore, a simple and efficient iterative algorithm is proposed to solve mixed discrete system. Some numerical examples are performed to verify the theoretical results. [ABSTRACT FROM AUTHOR]

A semilinear parabolic problem with a nonlocal Dirichlet boundary condition is studied. This article presents a new and very easy implementable numerical algorithm for computations. This is based on a suitable linearization in time. The derived algorithm is implicit and it does not need any iteration process to get a solution with the nonlocal boundary condition. The stability analysis has been performed and the convergence of approximations towards a solution of the continuous problem is shown. The uniqueness of a solution is proved. Error estimates for the time discretization are derived. [ABSTRACT FROM AUTHOR]