On one class of extremum problems for nonlinear operator systems (Q1968541)

The paper deals with the optimization problem in a reflexive Banach space \(X: I(u,y)\to \inf\), \(A(u,\alpha,y)=f\), \(F(u,y)\geq 0\), \( y\in K\subset X\), \(u\in U\subset \mathbf U,\) where \(A:U\times N\times X\to X^*\) and \(F:U\times X\to \mathbf R\cup \{+\infty\}\) are nonlinear mappings, \(f\in X^*.\) Using the penalization method the authors achieve the existence and regularity results for the solution \((u_0,y_0)\) of the optimization problem.