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Smoothing Approximation to the Square-Root Exact Penalty Function

Abstract In this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.