Brain-state-in-a-box neural networks with asymmetric coefficients

The equilibrium condition for brain-state-in-a-box neural networks is formulated as a variational inequality, well known in operations research and mathematical programming as a unified description of many equilibrium problems. In the case of symmetric coefficients, this variational inequality coincides with the first-order necessary conditions for minimality of the energy function of the neural net, but it is also valid if the coefficients are not symmetric. In that case, it leads to an appealing interpretation of equilibrium as a solution of a multiple-objective optimization problem. This study also provides conditions for uniqueness and global stability of the equilibrium state without assumption of symmetry.<>