Virtual convexity is a property that a function can have in localizing not only in a primal sense around a particular point but also in a dual sense relative to a subgradient at that point. In finite-dimensions it is tantamount to the subgradient mapping of the function being monotone locally around that primal-dual pair, which is indeed possible without local convexity.

This concept turns out to have fundamental implications in the understanding of sufficient conditions for local optimality that engender stability in support of numerical methodology. It is especially important for insights into augmented Lagrangians and their potential for producing a form of local duality that mimics the global duality enjoyed in convex optimization.


Time: 11:00 AM EST
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https://umich.zoom.us/j/95524251106?pwd=TUN5SnlVQzB5bGRtejZRU2NhVXpJUT09

Meeting ID: 955 2425 1106
Passcode: 491904

Here is the recording for anyone who missed it!
https://umich.zoom.us/rec/share/GLjhFpfQTXXKBXBEeYGKNJCJ1AzcPHfWjXyNKssv9wmIWCmhoUp_3qwVQpnf90_2.LlxdW6_ZxYoVi_SC
Speaker(s): Tyrrell Rockafellar (University of Washington, Seattle)