The Explicit Approximation Method for design optimization problems with implicit constraints

The Explicit Approximation Method for design optimization problems with implicit constraints is presented. This is a zero-order sequential approximation method. Only function values of the implicit constraint are needed, and no gradient calculation is required. The basic idea is to use engineering knowledge instead of purely numerical gradient information to form an explicit approximation to the implicit constraint. Design examples are presented to show how good explicit approximations to the implicit constraints can be formed, and a good and feasible, if not theoretically optimum, design can be found very efficiently by the Explicit Approximation Method using only zero-order information.