2,201 research outputs found
Exact penalty method for D-stationary point of nonlinear optimization
We consider the nonlinear optimization problem with least -norm
measure of constraint violations and introduce the concepts of the D-stationary
point, the DL-stationary point and the DZ-stationary point with the help of
exact penalty function. If the stationary point is feasible, they correspond to
the Fritz-John stationary point, the KKT stationary point and the singular
stationary point, respectively. In order to show the usefulness of the new
stationary points, we propose a new exact penalty sequential quadratic
programming (SQP) method with inner and outer iterations and analyze its global
and local convergence. The proposed method admits convergence to a D-stationary
point and rapid infeasibility detection without driving the penalty parameter
to zero, which demonstrates the commentary given in [SIAM J. Optim., 20 (2010),
2281--2299] and can be thought to be a supplement of the theory of nonlinear
optimization on rapid detection of infeasibility. Some illustrative examples
and preliminary numerical results demonstrate that the proposed method is
robust and efficient in solving infeasible nonlinear problems and a degenerate
problem without LICQ in the literature.Comment: 24 page
- β¦