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Digitale Medien

Continuous approximate solutions in parametric optimization (1989)

McClendon, J. F.

Springer

Acta applicandae mathematicae 15 (1989), S. 275-300

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ISSN: 1572-9036

Schlagwort(e): 90C31 ; 90D10 ; 54C60 ; Parametric optimization ; Nash equilibrium ; continuous solutions ; Serre multifunctions

Quelle: Springer Online Journal Archives 1860-2000

Thema: Mathematik

Notizen: Abstract The question of the existence of approximate solutions in parametric optimization is considered. Most results show that (under hypotheses) if a certain optimization problem has an approximate solution x 0 for a value p 0 of a parameter, then an approximate solution x=b(p) can be found for p in P, with b continuous, b(p 0)=x0, and any two such bs are homotopic. Some topological methods (use of fibrations) are used to weaken the usual ‘convex’ hypotheses of such results. An equisemicontinuity condition (relative to a constraint) is introduced to allow some noncompactness. The results are applied to get approximate Nash equilibrium results for games with some nonconvexity in the strategy sets.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF00047533

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