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This work discusses an approach, rst-order approximationand model management optimization (AMMO), for solving design optimization problems that involve computationally expensive simulations. AMMO maximizes the use of lower-delity, cheaper models in iterative procedures with occasional, but systematic, recourse to higherdelity, more expensive models for monitoring the progress of design optimization. A distinctive feature of the approach is that it is globally convergent to a solution of the original, high-delity problem. Variants of AMMO based on three nonlinear programming algorithms are demonstrated on a three-dimensional aerodynamic wing optimization problem and a two-dimensionalairfoil optimizationproblem. Euler analysison meshes of varying degrees of re nement provides a suite of variable-delity models. Preliminary results indicate threefold savings in terms of high-delity analyses for the three-dimensional problem and twofold savings for the two-dimensional problem. Nomenclature C D = drag coef cient C L = lift coef cient C l = rolling moment coef cient C M = pitching moment coef cient c E = equality constraints c I = inequality constraints f = objective function M 1 = freestream Mach number S = semispan wing planform area x; x L ; x U = design variables and bounds ® = angle of attack 1 = trust-region radius

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Analytical features of multidisciplinary optimization (MDO) problem formulations have signi cant practical consequences for the abilityof nonlinear programmingalgorithmsto solve the resulting computationaloptimization problems reliably and ef ciently. We explore this important but frequently overlooked fact using the notion of disciplinary autonomy. Disciplinary autonomy is a desirable goal in formulating and solving MDO problems; however, the resulting system optimization problems are frequently dif cult to solve. We illustrate the implications of MDO problem formulation for the tractability of the resulting design optimization problem by examining a representative class of MDO problem formulations known as collaborative optimization. We also discuss an alternative problem formulation, distributed analysis optimization, that yields a more tractable computational optimization problem. Nomenclature= system objective function g i = design constraints for D i l i = design variables local to D i min = minimize s = design variables shared by disciplines s.t. = subject to

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