Explicit model of dual programming and solving method for a class of separable convex programming problems. Issue 9 (2nd September 2019)

• Record Type: Journal Article
• Authors: Sui, YunKang; Peng, XiRong
• Is Part Of: Engineering optimization. Volume 51:Issue 9(2019)
• Page Start: 1604
• Page End: 1625
• Publication Date: 2019-09-02
• Subjects: Explicit dual objective function -- separable convex programming -- structural topology optimization -- dual sequential quadratic programming (DSQP) method -- method of moving asymptotes (MMA); Engineering design -- Periodicals; Mathematical optimization -- Periodicals; 620.0042
• DOI: 10.1080/0305215X.2018.1531988
• Languages: English
• ISSNs: 0305-215X

Abstract

ABSTRACT: An objective function for a dual model of nonlinear programming problems is an implicit function with respect to Lagrangian multipliers. This study aims to address separable convex programming problems. An explicit expression with respect to Lagrangian multipliers is derived for the dual objective function. The exact solution of the dual model can be achieved because an explicit objective function is more exact than an approximated objective function. Then, a set of improved Lagrangian multipliers can be used to obtain the optimal solution of the original nonlinear programming model. A corresponding dual programming and explicit model (DP-EM) method is proposed and applied to the structural topology optimization of continuum structures. The solution efficiency of the DPEM is compared with the dual sequential quadratic programming (DSQP) method and method of moving asymptotes (MMA). The results show that the DP-EM method is more efficient than the DSQP and MMA.