MA Cheng, LI Xun, YIU Ka-Fai Cedric, ZHANG Lian-sheng. A New Exact Penalty Function for Solving Constrained Finite Min-Max Problems[J]. Applied Mathematics and Mechanics, 2012, 33(2): 250-264. doi: 10.3879/j.issn.1000-0887.2012.02.010
Citation: MA Cheng, LI Xun, YIU Ka-Fai Cedric, ZHANG Lian-sheng. A New Exact Penalty Function for Solving Constrained Finite Min-Max Problems[J]. Applied Mathematics and Mechanics, 2012, 33(2): 250-264. doi: 10.3879/j.issn.1000-0887.2012.02.010

A New Exact Penalty Function for Solving Constrained Finite Min-Max Problems

doi: 10.3879/j.issn.1000-0887.2012.02.010
  • Received Date: 2011-03-31
  • Rev Recd Date: 2011-11-23
  • Publish Date: 2012-02-15
  • A new exact yet smooth penalty function to tackle constrained min-max problems was introduced. Using this new penalty function and adding just one extra variable, a constrained min-max problem was transformed into an unconstrained optimization one. It was proved that, under certain reasonable assumptions and when the penalty parameter was sufficiently large, the minimizer of this unconstrained optimization problem was equivalent to the minimizer of the original constrained one. Moreover, the local exactness property was also studied. The numerical results demonstrate that this penalty function method is an effective and promising approach for solving constrained finite min-max problems.
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