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
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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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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DOI: https://doi.org/10.1007/BF02250640