Nonlinear Lagrangian Functions and Applications to Semi-Infinite Programs

In this paper a nonlinear penalty method via a nonlinear Lagrangian function is introduced for semi-infinite programs. A convergence result is established which shows that the sequence of optimal values of nonlinear penalty problems converges to that of semi-infinite programs. Moreover a conceptual convergence result of a discretization method with an adaptive scheme for solving semi-infinite programs is established. Preliminary numerical experiments show that better optimal values for some nonlinear semi-infinite programs can be obtained using the nonlinear penalty method.