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Posted December 29, 2025
Last modified January 31, 2026

Colloquium Questions or comments?

R. Tyrrell Rockafellar, University of Washington
Dual Problems of Optimization

A surprising discovery in the early days of optimization theory was the prevalence of a new kind of duality. Typical problems then of interest, in which a linear function was to be minimized subject to constraints consisting of equations or inequalities imposed on other linear functions, couldn't be solved without simultaneously solving a partnered problem of maximization in the same category. The solutions to the two problems could be viewed moreover as the best strategies for two opponents is a sort of zero-sum game. This theme is now understood much more broadly as a feature of optimization theory that has been important not only in the design of solution algorithms, but also in extending mathematical analysis beyond the traditions of calculus.

Posted January 15, 2026

Colloquium Questions or comments?

Kumar Murty, University of Toronto
TBA