Exact Augmented Lagrangian Function for Nonlinear Programming Problems With Inequality Constraints

DU Xue-wu; ZHANG Lian-sheng; SHANG You-lin; LI Ming-ming

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Article Navigation > Applied Mathematics and Mechanics > 2005 > 26(12): 1493-1499

DU Xue-wu, ZHANG Lian-sheng, SHANG You-lin, LI Ming-ming. Exact Augmented Lagrangian Function for Nonlinear Programming Problems With Inequality Constraints[J]. Applied Mathematics and Mechanics, 2005, 26(12): 1493-1499.

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Exact Augmented Lagrangian Function for Nonlinear Programming Problems With Inequality Constraints

1.
Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;

Received Date: 2004-02-01
Rev Recd Date: 2005-05-31
Publish Date: 2005-12-15

Abstract

Abstract

An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed.Under suitable hypotheses,the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem.Furthermore,under some assumptions,the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem.Therefore,from the theoretical point of view,a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented.
- local minimizer,
- global minimizer,
- nonlinear programming,
- exact penalty function,
- augmented Lagrangian function

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References(14)

References

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