Abstract
By using the regularized gap function for variational inequalities, we introduce a new penalty function P α(x) for the problem of minimizing a twice continuously differentiable function in a closed convex subset of the n-dimensional space \(\mathbb{R}^n\). Under certain assumptions, it is shown that any stationary point of the penalty function P α(x) satisfies the first-order optimality condition of the original constrained minimization problem, and any local (or global) minimizer of P α(x) on \(\mathbb{R}^n\) is a locally (or globally) optimal solution of the original optimization problem.
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Li, W., Peng, J. Exact Penalty Functions for Constrained Minimization Problems via Regularized Gap Function for Variational Inequalities. J Glob Optim 37, 85–94 (2007). https://doi.org/10.1007/s10898-006-9038-8
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DOI: https://doi.org/10.1007/s10898-006-9038-8