Explicit model of dual programming and solving method for a class of separable convex programming problems

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 f...

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Bibliographic Details
Published in:Engineering optimization 2019-09, Vol.51 (9), p.1604-1625
Main Authors: Sui, YunKang, Peng, XiRong
Format: Article
Language:English
Subjects:
Asymptotes
Convexity
dual sequential quadratic programming (DSQP) method
Explicit dual objective function
Mathematical programming
method of moving asymptotes (MMA)
Multipliers
Nonlinear programming
Quadratic programming
separable convex programming
structural topology optimization
Topology optimization
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Summary: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.
ISSN:0305-215X
1029-0273
DOI:10.1080/0305215X.2018.1531988