27 Oct 2020
29 Oct 2020
"Conic, especially copositive optimization" by Prof. I. M. Bomze
Timetable: 8 hrs.
The course will be held online (link Zoom will be comunicated).
Calendar of the lectures
Tuesday October 27, 2020, 16:00
Wednesday October 28, 2020, 10:00-12:00
Thursday October 29, 2020, 10:00-12:00 and 15:00-17:00
Speaker: Prof. I. M. Bomze
Title: Conic, especially copositive optimization
Quite many combinatorial and some important non-convex continuous optimization
problems admit a conic representation, where the complexity of solving non-
convex programs is shifted towards the complexity of sheer feasibility (i.e.,
membership of the cone which is assumed to be a proper convex one), while
structural constraints and the objective are all linear. The resulting problem
is therefore a convex one, and still equivalent to some NP-hard problems with
inefficient local solutions despite the fact that in the conic formulation,
all local solutions are global.
Using characterizations of copositivity, one arrives at various
approximations. However, not all of these are tractable with current
technology. In this course, we will address some approaches on which tractable
SDP- or LP-approximations, and also branch-and-bound schemes, may be based.
This way, good tractable bounds can be achieved which serve as quality control
for any primal-feasible algorithm. But which one should be employed?
Complementing above (dual) approach, we will, mainly as one example, address a
classical yet not widely known first-order approach for poly/posynomial
optimization under simplex constraints, embedded in some general optimization
principles for iterative primal methods.
|Online, University of Padova