Abstract
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 optimization approaches: (i) general non-linear optimization, (ii) optimality criteria method, (iii) non-linear semidefinite programming, and (iv) polynomial optimization. We show that polynomial optimization solves the frame structure optimization to global optimality by building the (moment-sums-of-squares) hierarchy of convex linear semidefinite programming problems, and it also provides guaranteed lower and upper bounds on optimal design. Finally, we solve three sample optimization problems and conclude that the local optimization approaches may indeed converge to local optima, without any solution quality measure, 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.
Highlights
Designing economical, efficient, and sustainable structures represents a major challenge of the contemporary society
We develop four different methods in Section 2: (i) general non-linear optimization solved by the interior-point method of fmincon, (ii) the first-order optimality criteria (OC) method [1, 5], (iii) reformulation of the problem into a non-linear semidefinite program (NSDP) solved by PenLab [6], and (iv) a suitably modified polynomial optmization (PO) problem (iii) solved globally using polynomial optimization methods [7] and the Mosek [8] optimizer
We show that the latter PO approach generates guaranteed lower and upper bounds on the solution, providing a means of assessing the design quality
Summary
Efficient, and sustainable structures represents a major challenge of the contemporary society. We develop four different methods in Section 2: (i) general non-linear optimization solved by the interior-point method of fmincon, (ii) the first-order optimality criteria (OC) method [1, 5], (iii) reformulation of the problem into a non-linear semidefinite program (NSDP) solved by PenLab [6], and (iv) a suitably modified polynomial optmization (PO) problem (iii) solved globally using polynomial optimization methods [7] and the Mosek [8] optimizer We show that the latter PO approach generates guaranteed lower and upper bounds on the solution, providing a means of assessing the design quality.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
