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Local minimizer of a nonconvex quadratic programming problem

Ein Verfahren zur lokalen Minimierung nichtkonvexer quadratischer Programme

Abstract

A modified Beale's algorithm is described which computes the local minimizer of any quadratic objective function subject to linear constraints. Some extensions are given, first of all the possibility of movement to the neighbouring local minimizer with a reduced objective function value in some special cases.

Zusammenfassung

Es wird ein modifizierter Beale Algorithmus zur Bestimmung eines lokalen Extremums eines beliebigen quadratischen Programms bei linearen Restriktionen vorgestellt. Dazu werden einige Erweiterungen angegeben, etwa die Möglichkeit zu einem benachbarten lokalen Minimum mit kleinerem Zielfunktionalswert überzugehen.

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References

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    Beale, E. M. L.: On Minimizing a convex function subject to linear inequalities. J. Roy. Statist. Soc.17, 173–184. (1955).

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    Beale, E. M. L.: On quadratic programming. Naval. Res. Logistics Quarterly6: 227–243. (1957)

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    Abadie, J.: Nonlinear programming. Amsterdam: North-Holland. 1967.

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    Mráz, F.: Solving a noncovexx quadratic programming problem. Sborník PFČ. Budějovice 1980, 67–83 (in czech).

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Mráz, F. Local minimizer of a nonconvex quadratic programming problem. Computing 45, 283–289 (1990). https://doi.org/10.1007/BF02250640

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AMS Subject Classification

  • 90C20

Key words

  • Quadratic programming problem
  • local minimizer