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SUMMARY:Tiến-Sơn Phạm (University of Dalat)
DTSTART:20200603T070000Z
DTEND:20200603T080000Z
DTSTAMP:20260422T091823Z
UID:VAWebinar/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VAWebinar/1/
 ">Openness\, Hölder metric regularity and Hölder continuity properties o
 f semialgebraic set-valued maps</a>\nby Tiến-Sơn Phạm (University of 
 Dalat) as part of Variational Analysis and Optimisation Webinar\n\n\nAbstr
 act\nGiven a semialgebraic set-valued map with closed graph\, we show that
  it is Hölder metrically subregular and that the following conditions are
  equivalent:\n\n(i) the map is an open map from its domain into its range 
 and the range of is locally closed\;\n\n(ii) the map is Hölder metrically
  regular\;\n\n(iii) the inverse map is pseudo-Hölder continuous\;\n\n(iv)
  the inverse map is lower pseudo-Hölder continuous.\n\nAn application\, v
 ia Robinson’s normal map formulation\, leads to the following result in 
 the context of semialgebraic variational inequalities: if the solution map
  (as a map of the parameter vector) is lower semicontinuous then the solut
 ion map is finite and pseudo-Holder continuous. In particular\, we obtain 
 a negative answer to a question mentioned in the paper of Dontchev and Roc
 kafellar [Characterizations of strong regularity for variational inequalit
 ies over polyhedral convex sets. SIAM J. Optim.\, 4(4):1087–1105\, 1996]
 . As a byproduct\, we show that for a (not necessarily semialgebraic) cont
 inuous single-valued map\, the openness and the non-extremality are equiva
 lent. This fact improves the main result of Pühn [Convexity and openness 
 with linear rate. J. Math. Anal. Appl.\, 227:382–395\, 1998]\, which req
 uires the convexity of the map in question.\n
LOCATION:https://researchseminars.org/talk/VAWebinar/1/
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