### Optimization and Systems Theory Seminar

February 7, 1997, 11.00-12.00

** Ann-Brith Strömberg**,

Division of Optimization,

Department of Mathematics,

Linköping University

####
Ergodic, primal convergence in dual subgradient schemes for
convex programming

Lagrangean dualization and subgradient optimization techniques are
frequently used within the field of computational optimization for
finding approximate solutions to large, structured optimization
problems. The dual subgradient scheme does not automatically produce
primal feasible solutions; there is an abundance of techniques for
computing such solutions (via penalty functions, tangential
approximation schemes, or the solution of auxiliary primal programs),
all of which require a fair amount of computational effort. We
present a procedure which, at minor cost produces an ergodic sequence
of Lagrangean subproblem solutions that converges to the primal
optimal set, within a dual subgradient scheme for the solution of
convex programs. Numerical experiments performed on a traffic
equilibrium assignment problem under road pricing, show that the
computation of the ergodic sequence, results in a considerable
improvement in the quality of the primal solutions obtained, compared
to those obtained by the basic subgradient scheme.

Calendar of seminars

*Last update: January 16, 1997 by
Anders Forsgren,
andersf@math.kth.se.
*