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SUMMARY:Generalized Conditional Gradient with Augmented Lagrangian for Com
 posite Minimization - Exact and Inexact Perspectives - Antonio Silveti Fal
 ls\, ENSICAEN France
DTSTART:20191009T150000Z
DTEND:20191009T160000Z
UID:TALK131173@talks.cam.ac.uk
CONTACT:Jingwei Liang
DESCRIPTION:We propose a splitting scheme which hybridizes generalized con
 ditional gradient with a proximal step\, which we call CGALP algorithm\, f
 or minimizing the sum of three proper convex and lower-semicontinuous func
 tions in real Hilbert spaces. The minimization is subject to an affine con
 straint\, that allows in particular to deal with composite problems (sum o
 f more than three functions) in a separate way by the usual product space 
 technique. While classical conditional gradient methods require Lipschitz-
 continuity of the gradient of the differentiable part of the objective\, C
 GALP needs only differentiability (on an appropriate subset)\, hence circu
 mventing the intricate question of Lipschitz continuity of gradients. For 
 the two remaining functions in the objective\, we do not require any addit
 ional regularity assumption. The second function\, possibly nonsmooth\, is
  assumed simple\, i.e.\, the associated proximal mapping is easily computa
 ble. For the third function\, again nonsmooth\, we just assume that its do
 main is weakly compact and that a linearly perturbed minimization oracle i
 s accessible. Finally\, the affine constraint is addressed by the augmente
 d Lagrangian approach. We discuss both exact and inexact (stochastic) vari
 ants of the algorithm.
LOCATION:MR21\, Centre for Mathematical Sciences
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