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SUMMARY:Jon Lee (University of Michigan)
DTSTART:20210525T150000Z
DTEND:20210525T153000Z
DTSTAMP:20260415T002509Z
UID:MIP2021/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MIP2021/5/">
 Gaining or Losing Perspective for Piecewise-Linear Under-Estimators of Con
 vex Univariate Functions</a>\nby Jon Lee (University of Michigan) as part 
 of Mixed Integer Programming Workshop 2021\n\n\nAbstract\nWe study MINLO (
 mixed-integer non-linear optimization) formulations of the disjunction x 
 ∈ {0} ∪ [l\, u]\, where z is a binary indicator of x ∈ [l\,u] (0 ≤
  l < u)\,  and y "captures" f(x)\, which is assumed to be convex and posit
 ive on its domain [l\, u]\, but otherwise y=0 when x=0. This model is very
  useful in non-linear combinatorial optimization\, where there is a fixed 
 cost of operating an activity at level x in the operating range [l\, u]\, 
 and then there is a further (convex) variable cost f(x). In particular\, w
 e study relaxations related to the perspective transformation of a natural
  piecewise-linear under-estimator of f\, obtained by choosing linearizatio
 n points for f. Using 3-d volume (in (x\,y\,z)) as a measure of the tightn
 ess of a convex relaxation\, we investigate relaxation quality as a functi
 on of f\, l\, u\, and the linearization points chosen. We make a careful i
 nvestigation for convex power functions f(x) := xp\, p > 1.  \n\nThis is j
 oint work with Daphne Skipper\, Emily Speakman\, and Luze Xu.\n
LOCATION:https://researchseminars.org/talk/MIP2021/5/
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