A COMPARISON OF OPTIMALITY CRITERIA METHODS FOR STRESS AND DISPLACEMENT CONSTRAINTS

Optimality criteria (OC) methods and the closely related dual method h ave become one of the most important class of optimization algorithms used in the practice of structural optimization. Since this class of a lgorithms search the optimum in the dual space of the Lagrange multipl iers corresponding to the active constraints, the computational cost o f the optimization is determined mostly by the number of active constr aints. The efficiency of OC methods has been greatly improved recently by an OC method termed DCOC, which searches for the optimum in a usua lly much smaller dual subspace corresponding to only displacement mult ipliers. However, the relation of the DCOC with traditional OC methods is not clear, and therefore it is still difficult, even for people fa miliar with OC methods, to understand DCOC algorithm. This paper shows that the DCOC algorithm can be directly obtained from traditional OC methods, which provides insights into the method. Additionally, a deri vative-based version of DCOC is developed which also helps in the unde rstanding of the method.