An objectivefunction 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 ex...
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An objectivefunction 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 dualobjectivefunction. The exact solution of the dual model can be achieved because an explicitobjectivefunction is more exact than an approximated objectivefunction. 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.
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