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Abstract: This paper deals with the numerical solution of optimal control problems, where the state equations are given by the fourth order elliptic partial differential equations. An iterative algorithm for this class of problems is developed. This new proposal is obtained by combining the Conjugate Gradient Method (CGM) with the Boundary Element Method (BEM) and Multiple Reciprocity Method (MRM). The local error estimates based on the stability of this scheme in the norm, norm and norm are obtained. Finally, the numerical results on a test case show that this method is correct and feasible. [Copyright &y& Elsevier]