Discussed is an optimization problem of the form \[ \text{Min}_x \sum^m_{i=1} c_i x_i \] subject to relational constraints \[ {\mathbf x}\in X(A,{\mathbf b})= \{{\mathbf x}\in [0,1]^m\mid{\mathbf x}\circ A={\mathbf b}\}, \] where \(A\) is a \(m\)-by-\(n\) fuzzy relation (matrix) and \(b\) is an \(n\)-dimensional vector in the \([0,1]^n\) hypercube. The composition operator \((\circ)\) is \({\mathbf x}\) and \(A\) is realized by the max-t convolution with “t” standing for a certain continuous t-norm. The study is concerned with the optimization realized for the composition operator involved continuous Archimedean t-norms. For this case designed is an algorithm for determining a solution to the above stated optimization problem. Numerical illustrative examples are provided.