New year, new plans

First year's research has lead us to a refinement of  our goals.

Regarding the scalability of moment relaxations for the optimization of large power networks, we have found some interesting decompositions for the moment matrix leading to new relaxations reducing the computational effort while keeping the tightness of moment relaxations. Following up with this work, we now proceed to consider the sparsity of the network in order to reduce the number of variables in the programs.

We are also interested in the addition of discrete variables to power network optimization problems. We have already implemented some nonlinear, nonconvex, approaches noticing that the solutions are suboptimal. Now, we proceed to apply what we learn about convex optimization to develop new approaches that allow us to find better solutions in least computational time possible.

Tackling real-world problems is always a good motivation. This is the case for me as I have the opportunity to participate within the power network design team at Artelys. The task to be fulfilled is the solution of a subproblem arising in the design of power networks. Combinatorial nature of this problem makes it challenging... and fun to work with.