An optimization algorithm based on the method of feasible directions

Abstract

The theory and implementation of an optimization algorithm code based on the method of feasible directions are presented. Although the method of feasible directions was developed during the 1960's, the present implementation of the algorithm includes several modifications to improve its robustness. In particular, the search direction is generated by solving a quadratic program which uses an interior method based on a variation of Karmarkar's algorithm. The constraint thickness parameter is dynamically adjusted to yield usable-feasible directions. The theory is discussed with emphasis on the important and often overlooked role played by the various parameters guiding the iterations within the program. Also discussed is a robust approach for handling infeasible starting points. The code was validated by solving a variety of structural optimization test problems that have known solutions (obtained by other optimization codes). A variety of problems from different infeasible starting points has been solved successfully. It is observed that this code is robust and accurate. Further research is required to improve its numerical efficiency while retaining its robustness.