On optimum design of frame structures
Résumé
Optimization of frame structures is formulated as a non-convex optimization problem,which is currently solved to local optimality. In this contribution, we investigate four optimizationapproaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefi-nite programming, and (iv) polynomial optimization. We show that polynomial optimization solves theframe structure optimization to global optimality by building the (moment-sums-of-squares) hierarchyof convex linear semidefinite programming problems, and it also provides guaranteed lower and upperbounds on optimal design. Finally, we solve three sample optimization problems and conclude that thelocal optimization approaches may indeed converge to local optima, without any solution quality mea-sure, or even to infeasible points. These issues are readily overcome by using polynomial optimization,which exhibits a finite convergence, at the prize of higher computational demands.