Extrapolating the current trends in Supercomputer development one can expect that there will be at least one Exascale machine (i,e, capable of $10^{18}$ flops peak performance by 2020. Indeed there is already a 10 Petaflop machine (The "K-Computer" in Kobe, Japan) with more in the pipeline.

If one simply multiplies current Petaflop machines by a factor of 1000, an Exascale machine can be expected to have some scary characteristics: $10^9$ cores, Power consumption of ~1GW, mean time to failure significantly below 1 day and memory accesses so expensive that flops will be almost for free by comparison.

There are some concrete suggestions (on the hardware side) of how these limitations can be overcome, however they will not make programming such a machine any easier. In particular the question remains of what (if any) numerical algorithms will actually scale to $10^9$ cores. Nevertheless past experience tells us that a machine that is bleeding edge in 2020 will probably be standard fare in 2030. The challenges posed by these machine characteristics will remain, and overcoming them is likely to dominate algorithm development in the decades to come.

This talk will present some of the challenges posed by Exascale computing with a particular emphasis on their impact on Optimization Algorithms.

I have been involved over the last two years with the European Exascale Software Initiative (EESI) - which is attempting identify where current software (i.e. middleware, operating systems, compilers/tools, algorithms) is inadequate for use on an Exascale machine and what effort is needed to bridge those gaps by 2020. I will present some of the findings and recommendations coming out of the working group on Numerical Algorithms and Libraries (which includes Optimization).

In particular I will discuss in what form optimization is likely to be used on such a system, what barriers there currently are to achieve performance and what likely future research avenues are to overcome those barriers.

I will by no means have definite answers to any of these questions, but hope that my talk leads to some interesting and stimulating discussions.