Abstract
This paper identifies necessary and sufficient conditions for a penalty method to yield an optimal solution or a Lagrange multiplier of a convex programming problem by means of a single unconstrained minimization. The conditions are given in terms of properties of the objective and constraint functions of the problem as well as the penalty function adopted. It is shown among other things that all linear programs with finite optimal value satisfy such conditions when the penalty function is quadratic.
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This work was performed while the author was with the Engineering-Economic Systems Department, Stanford University, Stanford, California.
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Bertsekas, D.P. Necessary and sufficient conditions for a penalty method to be exact. Mathematical Programming 9, 87–99 (1975). https://doi.org/10.1007/BF01681332
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DOI: https://doi.org/10.1007/BF01681332