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.


Ann-Brith Strömberg (contact)

Biträdande professor at Mathematical Sciences, Mathematics

Emil Gustavsson

Doktorand at Mathematical Sciences, Mathematics

Magnus Önnheim

Doktorand at Mathematical Sciences, Mathematics

Michael Patriksson

at Mathematical Sciences, Mathematics


Linköping University

Linköping, Sweden



Funding years 1998–2020

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