BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Mikhail Solodov (IMPA Rio de Janeiro)
DTSTART:20210524T133000Z
DTEND:20210524T143000Z
DTSTAMP:20260423T035032Z
UID:OWOS/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OWOS/48/">Re
 gularized Smoothing for Solution Mappings of Convex Problems\, with Applic
 ations to Two-Stage Stochastic Programming and Some Hierarchical Problems<
 /a>\nby Mikhail Solodov (IMPA Rio de Janeiro) as part of One World Optimiz
 ation seminar\n\n\nAbstract\nMany modern optimization problems involve in 
 the objective function solution mappings or\noptimal-value functions of ot
 her optimization problems.\nIn most/many cases\, those solution mappings a
 nd optimal-value functions are nonsmooth\,\nand the optimal-value function
  is also possibly nonconvex (even if the defining data\nis smooth and conv
 ex).\nMoreover\, stemming from solving optimization problems\, those solut
 ion mappings and\nvalue-functions are usually not known explicitly\, via a
 ny closed formulas. Hence\,\nthere is no formula to differentiate (even in
  the sense of generalized derivatives).\nThis presents an obvious challeng
 e for solving the "upper" optimization problem\,\nas derivatives therein c
 annot be computed.\n\nWe present an approach to regularize and approximate
  solution mappings of fully\nparametrized convex optimization problems tha
 t combines interior penalty (log-barrier)\nwith Tikhonov regularization. B
 ecause the regularized solution mappings are single-valued\nand smooth und
 er reasonable conditions\, they can also be used to build a computationall
 y\npractical smoothing for the associated optimal-value function.\n\nOne m
 otivating application of interest is two-stage (possibly nonconvex) stocha
 stic\nprogramming. In addition to theoretical properties\, numerical exper
 iments are presented\,\ncomparing the approach with the bundle method for 
 nonsmooth optimization.\n\nAnother application is a certain class of hiera
 rchical decision problems\nthat can be viewed as single-leader multi-follo
 wer games.\nThe objective function of the leader involves the decisions of
  the followers (agents)\,\nwhich are taken independently by solving their 
 own convex optimization problems.\nWe show how our approach is applicable 
 to derive both agent-wise and scenario-wise\ndecomposition algorithms for 
 this kind of problems.\nNumerical experiments and some comparisons with th
 e complementarity solver PATH\nare shown for the two-stage stochastic Walr
 asian equilibrium problem.\n\nThe address and password of the zoom room of
  the seminar are sent by e-mail on the mailinglist of the seminar one day 
 before each talk\n
LOCATION:https://researchseminars.org/talk/OWOS/48/
END:VEVENT
END:VCALENDAR