A globally convergent sequential convex programming using an enhanced two-point diagonal quadratic approximation for structural optimization

• Published in: Structural and multidisciplinary optimization Vol. 50; no. 5; pp. 739 - 753
• Main Authors: Park, Seonho, Jeong, Seung Hyun, Yoon, Gil Ho, Groenwold, Albert A., Choi, Dong-Hoon
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014; Springer Nature B.V
• Subjects: Algorithms; Approximation; Computational geometry; Computational Mathematics and Numerical Analysis; Convergence; Convexity; Engineering; Engineering Design; Filtration; Mathematical programming; Nonlinear programming; Reduction; Research Paper; Theoretical and Applied Mechanics; Topology optimization; Diagonal quadratic approximation (DQA); Conservatism; Sequential convex programming (SCP); Enhanced two-point diagonal quadratic approximation (eTDQA); Filter method
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-014-1084-0

In this study, we propose a sequential convex programming (SCP) method that uses an enhanced two-point diagonal quadratic approximation (eTDQA) to generate diagonal Hessian terms of approximate functions. In addition, we use nonlinear programming (NLP) filtering, conservatism, and trust region reduction to enforce global convergence. By using the diagonal Hessian terms of a highly accurate two-point approximation, eTDQA, the efficiency of SCP can be improved. Moreover, by using an appropriate procedure using NLP filtering, conservatism, and trust region reduction, the convergence can be improved without worsening the efficiency. To investigate the performance of the proposed algorithm, several benchmark numerical examples and a structural topology optimization problem are solved. Numerical tests show that the proposed algorithm is generally more efficient than competing algorithms. In particular, in the case of the topology optimization problem of minimizing compliance subject to a volume constraint with a penalization parameter of three, the proposed algorithm is found to converge well to the optimum solution while the other algorithms tested do not converge in the maximum number of iterations specified.