. . "Nozzle design." . . "Aerodynamics." . . "Optimization." . . . . "Abstract: \"An all-at-once reduced Hessian Successive Quadratic Programming (SQP) scheme has been shown to be efficient for solving aerodynamic design optimization problems with a moderate number of design variables [1]. This paper extends this scheme to allow solution refining. In particular, we introduce a reduced Hessian refining technique that is critical for making a smooth transition of the Hessian information from coarse grids to fine grids. Test results on a nozzle design using quasi-one-dimensional Euler equations show that through solution refining the efficiency and the robustness of the all-at-once reduced Hessian SQP scheme are significantly improved.\""@en . . . . . . "Aerodynamic design optimization via reduced Hessian SQP with solution refining"@en . . . . . . . . . . . . "Design analysis." . .