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SUMMARY:Dr. Jan Harold Alcantara (RIKEN\, Japan)
DTSTART:20240227T060000Z
DTEND:20240227T070000Z
DTSTAMP:20260423T021435Z
UID:MAC8028/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAC8028/16/"
 >Theoretical smoothing frameworks for nonsmooth bilevel optimization probl
 ems</a>\nby Dr. Jan Harold Alcantara (RIKEN\, Japan) as part of Trends in 
 Mathematical Research\n\nLecture held in NTNU Gongguan S506.\n\nAbstract\n
 The optimal value function approach provides a useful reformulation of the
  bilevel optimization problem\, but its utility is often hindered by the n
 onsmoothness of the value function even in cases when the associated lower
 -level function is smooth. In this talk\, we present two smoothing strateg
 ies for the value function associated with lower-level functions that are 
 not necessarily smooth but are Lipschitz continuous. The first method empl
 oys a quadratic regularization approach for partially convex lower-level f
 unctions\, while the second utilizes entropic regularization for general l
 ower-level objective functions. Meanwhile\, the property known as gradient
  consistency is crucial in ensuring that a designed smoothing algorithm is
  globally subsequentially convergent to stationary points of the equivalen
 t reformulation of the bilevel problem. With this in mind\, we show that t
 he proposed smooth approximations satisfy the gradient consistent property
  under certain conditions on the lower-level function.\n
LOCATION:https://researchseminars.org/talk/MAC8028/16/
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