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In this paper, a model based on constraint convex optimization is proposed for the radiation pattern synthesis in cylindrical and spherical microstrip conformal array antennas. The optimization algorithm is modeled to decrease the Euclidean distance between the obtained radiation pattern of the deformed array and the desired radiation pattern of the planar array by calculating the suitable amplitude and phase values for the individual array patches. Four prototypes of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>×</mo><mn>4</mn></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>×</mo><mn>5</mn></mrow></semantics></math></inline-formula> microstrip patch array antenna are used as the radiating elements which are deformed from planar arrangement and placed on the faces of prescribed spherical and cylindrical shapes with various radii of curvatures. The results reveal that the performance of optimization algorithm performs better in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>×</mo><mn>5</mn></mrow></semantics></math></inline-formula> array, followed by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><mo>×</mo><mn>4</mn></mrow></semantics></math></inline-formula> array, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>×</mo><mn>3</mn></mrow></semantics></math></inline-formula> array, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>×</mo><mn>2</mn></mrow></semantics></math></inline-formula> array. However, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>×</mo><mn>5</mn></mrow></semantics></math></inline-formula> array provides more degrees of freedom for tuning the radiation pattern in desired form. The <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mo>×</mo><mn>5</mn></mrow></semantics></math></inline-formula> array computes suitable amplitude and phase values for the radiating elements of the array, which restore the radiation pattern in terms of mainlobe reconstruction, null locations, sidelobe levels, up to the deformation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>20</mn><mo> </mo><mi>cm</mi></mrow></semantics></math></inline-formula> in both spherical and cylindrical configurations of conformal array. The proposed optimization technique when applied to conformal antenna array offers fast computational speed and good convergence accuracy for radiation pattern synthesis, which can be useful for various engineering applications.