Considered is a problem of non-linear programming in the form \(g_ e(x)\leq 0\), \(e=1,2,...,M\), f(x)\(\to \min\), where g and f are non-linear functions of the independent variable \(x=\{x_ 1,x_ 2,...,x_ t,...,x_ n\}\). We then define the penalty function \(F=\sum_{e}g^+_ e\), where \(g_ e>0\to g^+_ e=g_ e\), \(g_ e\leq 0\to g^+_ e=0\), and by an arbitrary searching program S the lowermost point will be searched for on the F surface with the ordinate \(F=0\) that defines \((g_ e\leq 0\), \(e=1,2,...,M)\) the feasible region. After reaching this feasible point designate as \(x_ 1\) a suitable limitation is made in the form \(g_{M+1(j)}(x)=f(x)+[-f(x_ j)+{\bar \Delta}]\), where \({\bar \Delta}\) is the chosen positive constant. Let this limitation be introduced into the system forming the penalty function F, and again the feasible point is being searched for, designate now \(x_ 2\). After it is found it is substituted for \(x_ j\) in the last equation thus forming the new function \(g_{M+1(j)}\), etc. It is thus obvious that the feasible point \(x_ j\) is being found; then the function f is raised by \({\bar \Delta}\) and again the feasible point \(x_{j+1}\) is being searched for. The last point from the sequence of feasible points found in this way is then obviously the extreme that is being searched for.