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An Approximate Exact Penalty for Vector Inequality-Constrained Minimization Problems

Abstract

In this paper, we use the penalty approach in order to study a class of vector inequality-constrained minimization problems on Banach spaces. A penalty function is said to have the generalized exact penalty property if there is a penalty coefficient for which approximate solutions of the unconstrained penalized problem are close enough to approximate solutions of the corresponding constrained problem. For our class of problems, we establish the generalized exact penalty property and obtain an estimation of the exact penalty.

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Correspondence to Alexander J. Zaslavski.

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Zaslavski, A.J. An Approximate Exact Penalty for Vector Inequality-Constrained Minimization Problems. Vietnam J. Math. 42, 499–508 (2014). https://doi.org/10.1007/s10013-014-0077-z

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  • DOI: https://doi.org/10.1007/s10013-014-0077-z

Keywords

  • Approximate solution
  • Banach space
  • Minimization problem
  • Penalty function

Mathematics Subject Classification (1991)

  • 49M37
  • 90C30