HANDLING DIFFICULT EQUALITY CONSTRAINTS IN DIRECT SEARCH OPTIMIZATION

Difficult equality constraints can readily be handled in direct search optimisation by means of a quadratic penalty function containing shif ting terms. By using a multi-pass direct search optimisation method, w here the shifting terms are updated after every pass, convergence to t he optimum is systematic. At the optimum, twice the product of each sh ifting term and the penalty function factor gives the Lagrange multipl ier associated with that particular equality constraint. Two numerical examples show that the proposed procedure is computationally efficien t. The range over which the penalty function factor can be chosen to o btain convergence to the global optimum is very large, making this an attractive way of optimising systems having both inequality constraint s and difficult equality constraints.