The paper is devoted to the problem of finding the global minimum of a lower semicontinuous and robust function \(f\). A set is robust if \(\text{cl}(D)=\text{cl}(\text{int}(D))\) and \(f\) is robust if its epigraph is robust. An optimality condition using topological measures \(\mu\) (nonempty open sets should have positive measure) is given in the form: \(\mu(H_ c)=0\), where \(H_ c=\{x:f(x)\leq c\}\neq\varnothing\). On this basis an algorithm for finding the global minimum is proposed --- it uses the mean value of \(f\) over the sets \(H_ c\), for decreasing \(c\). A reference for an industrial application is given.