Two-point constraint approximation in structural optimization

The use of constraint approximations is recognized as a primary means of achieving computational efficiency in structural optimization. Existing approximation methods are based upon the value of the constraint function and its derivatives at a single point. The present paper explores the use of approximations based upon the value of the constraint and its derivative at two points. Several candidate approximations are suggested and tested for randomly generated rational constraint functions. Several of the approximations prove to be superior to the single-point approximations.