Date:  2nd April (Tue) 10:30-11:30
Place: #235,  Engineering Bldg.6
Speaker: Ting Kei Pong  (the Hong Kong Polytechnic University)

Title: Deducing Kurdyka-Łojasiewicz exponent of optimization

Abstract: Kurdyka-Łojasiewicz (KL) exponent is an important
quantity for determining the qualitative convergence
behavior of many first-order methods. In this talk, we
review some known connections between the KL exponent and
other important error bound concepts, and discuss some
calculus rules that allow us to determine the KL exponent of
new functions from functions with known KL exponent.
Specifically, we will show that KL exponents are preserved
under Lagrange relaxation and inf-projection, under mild
assumptions. This allows us to deduce, under suitable
assumptions, the KL exponent of many important convex or
nonconvex optimization models, such as group fused LASSO,
least squares with MCP or SCAD regularization, least squares
with rank constraint, and envelope functions such as the
Moreau envelope or the forward-backward envelope.
This is a joint work with Guoyin Li and Peiran Yu.
Date:  3rd April (Wed) 14:00-14:40
Place: #534,  Engineering Bldg.14
Speaker: Ting Kei Pong    (the Hong Kong Polytechnic University)
Title: Gauge optimization: Duality and polar envelope

Abstract: Gauge optimization seeks the element of a convex
set that is minimal with respect to a gauge function, and
arises naturally in various contemporary applications such
as machine learning and signal processing. In this talk, we
explore the gauge duality framework proposed by Freud. We
then define the polar envelope and discuss some of its
important properties. The polar envelope is a convolution
operation specialized to gauges, and is analogous to Moreau
envelope. We will highlight the important roles the polar
envelope plays in gauge duality and in the construction of
algorithms for gauge optimization.
This is joint work with Michael Friedlander and Ives Macêdo.