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The objective of this paper is to present a convex–concave optimization approach for solving the problem of a multistage launch vehicle ascent trajectory. The proposed method combines convex–concave decomposition and successive linearization techniques to generate a new sequence of convex subproblems to replace the original non-convex problem. Bernstein approximation is used to transform the chance constraints into convex ones. A h p -adaptive pseudospectral scheme is employed to discretize the optimal control problem into a nonlinear programming problem with less computation cost. The performance of the proposed strategy is compared against other typical techniques in a selection of test case scenarios. Numerical results demonstrate the viability of the method and show pros and cons of the proposed technique. • A noise-perturbed multi-stage launch vehicle trajectory optimization model is proposed. • The convex–concave decomposition method is applied to the multistage launch vehicle ascent problem. • The convex–concave decomposition and successive linearization methods allow for a reduction of the computational cost. • An extension to handle chance constraints based on Bernstein approximation approach is proposed. [ABSTRACT FROM AUTHOR]