@misc{SagnolBlancoSauvage2017, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {The Cone of Flow Matrices: Approximation Hierarchies and Applications}, issn = {1438-0064}, doi = {10.1002/net.21820}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64399}, year = {2017}, abstract = {Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices \$\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}\$, where \$\vec{1}_P\in\RR^n\$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over \$\mathcal{K}\$. This cone is intractable: we prove that the membership problem associated to \$\mathcal{K}\$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix \$X\in \operatorname{span} \mathcal{K}\$ as a linear combination of some \$\vec{1}_P\vec{1}_P^T\$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities.}, language = {en} } @misc{DuarteSagnolOliveira2015, author = {Duarte, Belmiro P.M. and Sagnol, Guillaume and Oliveira, Nuno M.C.}, title = {A robust minimax Semidefinite Programming formulation for optimal design of experiments for model parametrization}, issn = {1438-0064}, doi = {10.1016/B978-0-444-63578-5.50146-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-54626}, year = {2015}, abstract = {Model-based optimal design of experiments (M-bODE) is a crucial step in model parametrization since it encloses a framework that maximizes the amount of information extracted from a battery of lab experiments. We address the design of M-bODE for dynamic models considering a continuous representation of the design. We use Semidefinite Programming (SDP) to derive robust minmax formulations for nonlinear models, and extend the formulations to other criteria. The approaches are demonstrated for a CSTR where a two-step reaction occurs.}, language = {en} }