Lagrangian regularization approach to constrained optimization problems Original Research Article

This paper proposes a new regularization approach, referred to as the Lagrangian regularization approach, which aims to circumvent the nondifferentiability of a positively homogeneous function View the MathML sourceδ(·|R-m) in a conceptual unconstrained reformulation for constrained optimization problems. With the appropriate choices of regularizing function, we obtain a family of smooth functions that include, as special cases, the existing penalty and barrier functions. As such, our approach can be used as an instrumental tool to resolve the nondifferentiability of View the MathML sourceδ(·|R-m) as well as a unified way to construct penalty functions. For convex programming cases, we present its global convergence analysis.