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Journal of Optimization Theory and Applications

, Volume 12, Issue 3, pp 233–241 | Cite as

Global convergence for Newton methods in mathematical programming

  • J. W. Daniel
Article

Abstract

In constrained optimization problems in mathematical programming, one wants to minimize a functionalf(x) over a given setC. If, at an approximate solutionx n , one replacesf(x) by its Taylor series expansion through quadratic terms atx n and denotes byx n+1 the minimizing point for this overC, one has a direct analogue of Newton's method. The local convergence of this has been previously analyzed; here, we give global convergence results for this and the similar algorithm in which the constraint setC is also linearized at each step.

Keywords

Newton Method Global Convergence Local Convergence Constraint Qualification Quadratic Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • J. W. Daniel
    • 1
    • 2
  1. 1.Departments of Mathematics and of Computer SciencesThe University of Texas at AustinAustin
  2. 2.Center for Numerical AnalysisThe University of Texas at AustinAustin

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