We consider the problem \min\limits_{v\in\,C}J(v) min v ∈ C J ( v ) , where J J is the standard integral functional J(v) = \int_{\Omega} j(x,{\nabla v}) - \int_{\Omega} f(x)\,v(x), J ( v ) = ∫ Ω j ( x , ∇ v ) − ∫ Ω f ( x ) v ( x ) , defined in the Sobolev space W_0^{1,q}(\Omega) W 0 1 , q ( Ω ) . We study the convergence of the minima u u if we perturb the convex set C C in accordance with the Mosco convergence.