  In this paper, we introduce a nonlinear optimization problem whose objective
function is the convex log-sum-exp function and the feasible region is defined
as a system of fuzzy relational inequalities (FRI) defined by the Lukasiewicz
t-norm. Some necessary and sufficient conditions are derived to determine the
feasibility of the problem. The feasible solution set is characterized in terms
of a finite number of closed convex cells. Since the feasible solutions set of
FRIs is non-convex, conventional methods may not be directly employed. An
algorithm is presented for solving this nonlinear problem. It is proved that
the algorithm can find the exact optimal solution and an example is presented
to illustrate the proposed algorithm.
