Computational Optimization and Applications

, Volume 35, Issue 3, pp 375–398 | Cite as

On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

  • Zhiqing Meng
  • Chuangyin Dang
  • Xiaoqi Yang


In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient.


constrained optimization penalty function exact penalty function smoothing method ∈-feasible solution, optimal solution 


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.College of Business and AdministrationZhejiang University of TechnologyHangzhouChina
  2. 2.Department of Manufacturing Engineering & Engineering ManagementCity University of Hong KongKowloonHong Kong
  3. 3.Department of Applied MathematicsThe Hong Kong Polytechnic UniversityHung HomHong Kong

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