A self-adaptive penalty approach for nonlinear programming

For penalty approaches, it is extremely difficult to choose penalty parameter and penalty term to avoid ill-conditions. In this work, penalty techniques fornonlinear programming problems are revisited. A new penalty approach, which is called self-adaptive penalty method, is proposed. When penalty parameter and penalty term are considered, we adjust them according to the feedback information at each step (and the previous steps) in the new method so that the second information of the subproblem may be a semidefinite positive matrix whose conditioned number is not too large.