A METHOD FOR STRUCTURAL OPTIMIZATION WHICH COMBINES 2ND-ORDER APPROXIMATIONS AND DUAL TECHNIQUES

A structural optimization problem is usually solved iteratively as a s equence of approximate design problems. Traditionally, a variety of ap proximation concepts are used, but lately second-order approximation s trategies have received most interest since high quality approximation s can be obtained in this way. Furthermore, difficulties in choosing t uning parameters such as step-size restrictions may be avoided in thes e approaches. Methods that utilize second-order approximations can be divided into two groups; in the first, a Quadratic Programming (QP) su bproblem including all available second-order information is stated, a fter which it is solved with a standard QP method, whereas the second approach uses only an approximate QP subproblem whose underlying struc ture can be efficiently exploited. In the latter case, only the diagon al terms of the second-order information are used, which makes it poss ible to adopt dual methods that require separability. An advantage of the first group of methods is that all available second-order informat ion is used when stating the approximate problem, but a disadvantage i s that a rather difficult QP subproblem must be solved in each iterati on. The second group of methods benefits from the possibility of using efficient dual methods, but lacks in not using adl available informat ion. In this paper, we propose an efficient approach to solve the QP p roblems, based on the creation of a sequence of fully separable subpro blems, each of which is efficiently solvable by dual methods. This pro cedure makes it possible to combine the advantages of each of the two former approaches. The numerical results show that the proposed soluti on procedure is a valid approach to solve the QP subproblems arising i n second-order approximation schemes.