×

A Lagrangian penalty function method for monotone variational inequalities. (English) Zbl 0703.49011

The authors investigate a constrained variational inequality problem and use a penalty function method to convert it into simpler problems that need only be solved approximately. An algorithm is presented and results related to this show that under suitable conditions the solutions to the approximate problems will converge to a solution of the original problem as the approximation parameter tends to 0. An advantage of the penalty method used here is that in nondegenerate situations the penalty parameter avoids tending to 0 or \(\infty\). A condition under which the penalty function is exact is also given.
Reviewer: J.Murray

MSC:

49J40 Variational inequalities
49M30 Other numerical methods in calculus of variations (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] DOI: 10.1007/BF01681332 · Zbl 0325.90055 · doi:10.1007/BF01681332
[2] Gwinner J., Operations Research Verfahren 28 pp 374– (1978)
[3] Gwinner J., Optimization - Theory and Algorithms pp 197– (1981)
[4] DOI: 10.1007/BF01588250 · Zbl 0424.90057 · doi:10.1007/BF01588250
[5] DOI: 10.1016/0041-5553(86)90159-X · Zbl 0635.90073 · doi:10.1016/0041-5553(86)90159-X
[6] Oettli W., Advances in Mathematical Optimization 45 pp 130– (1988)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.