Description
CCOR Optimalizálási Szeminárium
We present iterative proximal point type algorithms for determining weakly efficient solutions to unconstrained convex vector optimization problems. After discussing the vector-minimization of a single cone-convex vector function by means of an inertial proximal point algorithm, we turn to the case when the objective function is the sum of a differentiable vector function with a nonsmooth cone-convex one. An inertial forward-backward method with memory effects based on recent advances in solving scalar convex optimization problems and monotone inclusions is proposed, by making use of some adaptive linear scalarization techniques. During the talk, the difficulties encountered while formulating the algorithm and proving its convergence will be stressed, while the related discussion of extending the celebrated FISTA method from scalar to vector optimization problems will be mentioned, too. Several (still unsolved) challenges in extending proximal point type methods from scalar to vector optimization problems will be addressed as well.
This talk is based on joint work with Radu Ioan Bot.
References
[1] H. Bonnel, A.N. Iusem, B.F. Svaiter: Proximal methods in vector optimization, SIAM J Optim 15:953–970, 2005
[2] R.I. Bot, S.-M. Grad: Inertial forward-backward methods for solving vector optimization problems, Optimization 67:959–974, 2018
[3] S.-M. Grad: A survey on proximal point type algorithms for solving vector optimization problems, in: H.H. Bauschke, R. Burachik, D.R. Luke (Eds.), "Splitting Algorithms, Modern Operator Theory, and Applications", Springer-Verlag, Cham, 269–308, 2019
For Zoom access please contact E.-Nagy Marianna (marianna.eisenberg-nagy[at]uni-corvinus.hu).