Abstract A numerical method to solve simultaneous design and control optimization problems is considered. Firstly, the simultaneous optimization problem in this paper is transformed into a new formulated nonlinear programming problem. Considering using a sequential quadratic programming method, the diagonal form of the Hessian matrix for the Lagrange function is introduced in a new formulation named Block Diagonal Hessian (BDH) method. Finally, the present method is applied to simultaneous spaceplane design and trajectory optimization problems for feasibility study of a future space transportation system. Through several calculations, the proposed BDH method is confirmed to be effective for simultaneous optimization problems.
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