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On the convergence of the projected gradient method (1993)

Dussault, J. P. ; Fournier, G.

Springer

Journal of optimization theory and applications 77 (1993), S. 197-208

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Details

ISSN: 1573-2878

Schlagwort(e): Nonlinear optimization ; convergence of ascent methods

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract We study the projected gradient algorithm for linearly constrained optimization. Wolfe (Ref. 1) has produced a counterexample to show that this algorithm can jam. However, his counterexample is only ℒ1(ℝ n ), and it is conjectured that the algorithm is convergent for ℒ2-functions. We show that this conjecture is partly right. We also show that one needs more assumptions to prove convergence, since we present a family of counterexamples. We finally give a demonstration that no jamming can occur for quadratic objective functions.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00940786

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