The earliest doubts of the validity of the Principle of the Excluded Middle (PEM) can be found in Brouwer’s notes for his dissertation. The actual formulation had to wait for the “Unreliability of the logical principles” paper one year later. It is a curious fact that in the dissertation Brouwer shrugged off the PEM as obvious and ‘uninformative’. He denied it mathematical significance, because...

In this paper, we consider a new formulation for stochastic mathematical programs with complementarity constraints and recourse. We show that the new formulation is equivalent to a smooth semi-infinite program that does no longer contain recourse variables. Optimality conditions for the problem are deduced and connections among the conditions are investigated. Then, we propose a combined Monte ...

The idea of the mini-course is to review the formulation of quantum theories from an advanced viewpoint, essentially based on the orthomodular lattice of elementary propositions due to von Neumann, discussing some fundamental ideas, mathematical tools and theorems in particular related to the representation of physical symmetries (Gleason, Wigner-Kadison, Stone Stone-von Neumann, Garding, Nelso...

This thesis concerns the use of reformulation techniques in mathematical programming. Optimization and decision problems can be cast into a formulation involving sets of known numerical parameters, decision variables whose value is to be determined as a result of an algorithmic process, one of more optional objective functions to be optimized and various sets of constraints, which can be either...