The paper considers different problem formulations of topology
optimization of discrete or discretized structures with
eigenvalues as constraints or as objective functions. We study
multiple load case formulations of minimum weight, minimum
compliance problems and of the problem of maximizing the minimal
eigenvalue of the structure including the effect of non-structural
mass. The paper discusses interrelations of the problems and, in
particular, shows how solutions of one problem can be derived from
solutions of the other ones. Moreover, we present equivalent
reformulations as semidefinite programming problems with the
property that, for the minimum weight and minimum compliance
problem, each local optimizer of these problems is also a global
one. This allows for the calculation of guaranteed global
optimizers of the original problems by the use of modern solution
techniques of semidefinite programming. For the problem of
maximization of the minimum eigenvalue we show how to verify the
global optimality and present an algorithm for finding a tight
approximation of a globally optimal solution. Numerical examples
are provided for truss structures. Examples of both academic and
larger size illustrate the theoretical results achieved and
demonstrate the practical use of this approach. We conclude with
an extension on multiple non-structural mass conditions.