Based on the Differential Transformation Method (DTM), a solution procedure for solving a class of nonlinear quadratic optimal control problems is presented in this paper. The reason for selecting this solution procedure is the less computational cost in comparison with the ordinary solution methods of original problem. First, the problem is converted to a two-point boundary value problem then the new problem is transferred into a set of algebraic equations by applying the differential transformation properties. By presenting the algorithmic solution procedure, two numerical examples are given to demonstrate the simplicity and efficiency of the new method.

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We consider optimal shape design problems defined by pairs of geometrical elements and control functions associated with linear or nonlinear elliptic equations. First, necessary conditions are illustrated in a variational form. Then by applying an embedding process, the problem is extended into a measure-theoretical one, which has some advantages. The theory suggests the development of a computational method consisting of the solution of a finitedimensional linear programming problem. Nearly optimal shapes and related controls can thus be constructed. Two examples are also given.

First, an extension of Pontryagin Maximum Principle in Infinite-Horizon, which was presented by Aseev and Kryazhimiskii, is explained. Since this method is applicable in optimal economical growth problems, for the first time several problems such as consumption and investment are solved. Moreover, for implementing Aseev and Kryazhimiskii 's method on Iranian economy, Luis Serven model is introduced. Then it is calibrated on Iranian economy during the years 1385-1415. By applying the described method, the optimal consumption and investment for maximizing the social welfare are demonstrated. Also the sensitivity analysis is discussed.

In this article, we present a new algorithm for solving Semi-Infinite Linear Programming (SILP) problems based on an artificial neural network concept. First the local reduction method for solving the SILP problems is introduced. Based on the local reduction method, the Karush-Kuhn-Tucker (KKT) conditions and gradient method are used to convert the SILP problem to an unconstrained optimization problem; then, a neural network model is constructed to solve it. Numerical example has been employed to indicate the accuracy of the new method.