Abstract
A readily implementable subgradient algorithm is given for minimizing a convex, but not necessarily differentiable, functionf subject to a finite number of linear constraints. It is shown that the algorithm converges to a solution, if any. The convergence is finite iff is piecewise linear.
Zusammenfassung
Ein Subgradientenalgorithmus für konvexe, nicht unbedingt differenzierbare Funktionen mit einer endlichen Anzahl von Nebenbedingungen wird angegeben. Es wird bewiesen, daß der Algorithmus gegen die Lösung konvergiert, wenn es eine Lösung gibt. Die Lösung wird im Fall einer stückweise linearen Funktion nach endlich vielen Schritten erreicht.
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This work was sponsored by Project CPBP-02-15.
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Kiwiel, K.C. A subgradient selection method for minimizing convex functions subject to linear constraints. Computing 39, 293–305 (1987). https://doi.org/10.1007/BF02239973
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DOI: https://doi.org/10.1007/BF02239973