### Antonio Frangioni (University of Pisa, Italy)

#### Large (un)structured master problems in decomposition algorithms and interior-point methods: friend or foe?

*Thursday 5 Febrary 2015 at 13.00, JCMB 4325A*

##### Abstract

Using multicommodity flow/network design problems as motivating examples, we
review some (more or less recent) developments in decomposition approaches for
large-scale structured optimization which lead to the notion that "the master
problem has to be large" for convergence to occur quickly. Besides, for
optimal performances the structure of the master problem may have to be
significantly different from the ones employed in by-the-book implementations,
requiring the use of general-purpose solvers (or the development of approaches
capable of "exploiting the structure of an unstructured problem"). This
highlights the importance of correctly choosing within the trade-off between
master problem size, and therefore computational cost, and the number of
iterations required to attain convergence (which, in turn, has an effect on
the average size of all the master problems solved). Which solution approach
is employed to solve the master problems is clearly very relevant in this
context. Interior-point methods may on one hand be promising candidates due to
several aspects (capability of exploiting different forms of structure in the
coefficient matrix, resilience to the introduction of nonlinear terms, good
influence on the quality of the generated dual solutions, outright
computational efficiency, ...), but on the other hand may be challenged by the
need of performing more complex reoptimizations than in the case of more
standard master problems. The seminar offers no answers to these issues, just
hopes to rise the right questions in front of the right audience.

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