An efficient feasible directions algorithm for design synthesis
A nonlinear optimization algorithm is described that combines the best features of the method of feasible directions and the generalized reduced gradient method. The algorithm uses the direction-finding subproblem from the method of feasible directions to find a search direction that is equivalent to that of the generalized reduced gradient method, but without the need to add a large number of slack variables associated with inequality constraints. This leads to a core-efficient algorithm for the solution of optimization problems with a large number of inequality constraints. Also, during the one-dimensional search, it is not necessary to separate the design space into dependent and independent variables using the present method. The concept of infrequent gradient calculations is introduced as a means of gaining further optimization efficiency. Finally, it is shown that, using the basic direction-finding algorithm contained in this method, the sensitivity of the optimum design with respect to problem parameters can be obtained without the need for second derivatives or Lagrange multipliers. The optimization algorithm and sensitivity analysis is demonstrated by numerical example.