Constrained Variable Metric Method With Feasible Directions

This paper proposes a new feasible direction algorithm based on the constrained variable metric method of Powell in order to handle the design optimization problmes which demand that all iterative points are feasible. The algorithm retains many advantages of the constrained variable metric method, makes use of the properties of the solutions of quadratic programming problems and information of iterative points to define feasible directions, and uses the monotonicity analysis to establish the linesearch strategy which is especially suitable for feasible direction algorithms and a simple and efficient method for finding feasible initial points. The numerical results presented in the paper demonstrate that its rate of convergence is faster than those of Powell’s method and another feasible direction algorithm of Herskovits and its iterative procedure avoids Maratos effect.