Nonsmooth convex optimization—theory and solution methodology

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)

Biträdande professor vid Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Emil Gustavsson

Doktorand vid Mathematics

Magnus Önnheim

Doktorand vid Chalmers, Mathematical Sciences, Algebra and geometry

Michael Patriksson

Professor vid Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Collaborations

Linköping University

Linköping, Sweden

Funding

Chalmers

Funding Chalmers participation during 1998–2020

Related Areas of Advance and Infrastructure

Transport

Areas of Advance

Energy

Areas of Advance

Basic sciences

Roots

More information

Latest update

2016-01-12