Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (7): 951-962.doi: https://doi.org/10.1007/s10483-012-1597-x

• Articles • Previous Articles    

New simple exact penalty function for constrained minimization

Fang-ying ZHENG1,2, Lian-sheng ZHANG2   

  1. 1. Department of Mathematical Sciences, Zhejiang Sci-Tech University, Hangzhou 310018, P. R. China;
    2. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China
  • Received:2011-04-18 Revised:2012-03-22 Online:2012-07-10 Published:2012-07-10
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Nos. 10571116 and 51075421)

Abstract: By adding one variable to the equality-or inequality-constrained minimization problems, a new simple penalty function is proposed. It is proved to be exact in the sense that under mild assumptions, the local minimizers of this penalty function are precisely the local minimizers of the original problem, when the penalty parameter is sufficiently large.

Key words: nonlinear control system, controllability, oriented manifold, invariant manifold, basic system, dynamics of rigid body, nonlinear programming, constrained minimization, local solution, exact penalty function

2010 MSC Number: 

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