Nonsmooth convex optimization—theory and solution methodology
Research Project
, 1998
– 2022
In a long series of projects, we study nonsmooth convex optimization problems. The topics studied include theory -mathematical and related complexity properties-as well as methodology development and convergence analyses. The problems studied are composed by linear and/or nonlinear convex functions and polyhedral and/or general convex sets. In particular, we study Lagrangean dual reformulations of convex optimization problems and methodology for their solution.
We have developed and analyzed generalized subgradient optimization methods. Further, since (Lagrangean) dual subgradient schemes do not automatically produce primal feasible solutions, we construct - at minor cost - an ergodic sequence of primal subproblem solutions which is shown to converge to the primal solution set. We have further elaborated with the construction of the primal ergodic sequences, in order to increase the convergence speed.
Participants
Ann-Brith Strömberg (contact)
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Emil Gustavsson
Mathematics
Magnus Önnheim
Chalmers, Mathematical Sciences, Algebra and geometry
Michael Patriksson
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Collaborations
Linköping University
Linköping, Sweden
Funding
Chalmers
Funding Chalmers participation during 1998–2020
Naturvetenskapliga Forskningsrådet
Funding Chalmers participation during 1998–2022
Related Areas of Advance and Infrastructure
Transport
Areas of Advance
Energy
Areas of Advance
Basic sciences
Roots