Direct Treatment of State Constraints in Aerodynamic Shape Optimization Using Simultaneous Pseudo-Time-Stepping

Introduction

In this chapter, we adopt a direct treatment of the state constraints in simultaneous pseudo-time-stepping method for the optimization problem. As discussed in the previous chapter, one can treat the constraints ‘indirectly’, e.g., by making some kind of transformation so that the constraints are added to the objective function (with some weighting) and the constrained problem is reduced to an unconstrained one. However, it is well known (see, for example, [43], subsection 7.2, pp.144) that the reduced problem may not correspond always to the original problem and the solution process may not be efficient one. Therefore, we discuss an alternative, direct way of treating the constraints.