Robust and probabilistic optimization methods with applications to truss structures

The work reported in this thesis is about one of the many branches of convex optimization: the truss structures design. A truss is a collection of bars which meet each other at certain points - the nodes - to form a planar or spatial lattice. Truss structures are ubiquitous and widespread in the industrialized and civil world; they appear as bridges, towers, roof supports, building exoskeletons, cranes and so on everywhere. The most famous and popular example of truss structure is the Eiffel tower, which has more than 15000 girders connected at over 30000 points. These numbers give the straightforward idea that it would be almost impossible (particularly in complex cases) and tedious to design a truss structures by hand; hence design algorithms are required. The philosophy at the basis of this thesis is to handle a robust or probabilistic truss structures design towards uncertainty associated to the data of the problem by providing to the processor the lattice geometry (i.e. position of nodes where the bars meet each other), the fixed nodes holding the structure and, finally, the external forces acting on the truss