In [J. Nedoma, Ann. Oper. Res. 47 (1993) 483–496], a method for optimizing a linear function on the solution set of a vague system of linear equations was proposed. In this paper, we deal with the so-called simultaneous version of this method. We show tha

The Lyapunov–Schmidt reduction is generalized such that it uniformly handles bothperfect and imperfect singularities. The results presented need neither very precise information about the location of the (near) singularities nor a precise knowledge of (near) null spaces.