The paper is devoted to the optimization of the multi-edge trajectory of a reusable space launcher, using an interior-point algorithm, combined with dedicated linear algebra solvers. We apply our tool to a simple model of multi-edge trajectory. Basically, the algorithm consists in Newton steps applied to the primal-dual formulation of the optimality system with logarithmic penalty of all inequality constraints. We have adopted the so-called dogleg procedure in order to globalize the algorithm. Our linear algebra tool is based on the band structure of the Jacobian, which (up to a doubling of bandsize) is compatible with the QR factorization (that, since it is based on rotations, has strong stability properties). Design parameters are dealt with a bilevel procedure within the linear algebra procedure. We define an inductive structure on this block matrices to describe the linear algebra. The interior-point methodology is used to treat path constraints in this method. In the single-edge case, a refinement procedure had been set up. This paper will not focus on this point, but we can say that the interior-point methodology allows refinement at any stage of the algorithm. This means that, for a given value of the logarithmic penalty parameter, we may reach a given target on integration errors, and hence, solve the penalized problem with a prescribed precision. After the presentation of this method, we validate it successfully on a multi-edge problem inspired from a two-stage-to-orbit concept.
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