An interior-point ℓ_1/2-penalty method for inequality constrained nonlinear optimization

In this paper, we study inequality constrained nonlinear programming problems by virtue of an ℓ1/2-penalty function and a quadratic relaxation. Combining with an interior-point method, we propose an interior-point ℓ1/2-penalty method. We introduce different kinds of constraint qualifications to establish the first-order necessary conditions for the quadratically relaxed problem. We apply the modified Newton method to a sequence of logarithmic barrier problems, and design some reliable algorithms. Moreover, we establish the global convergence results of the proposed method. We carry out numerical experiments on 266 inequality constrained optimization problems. Our numerical results show that the proposed method is competitive with some existing interior-point ℓ1-penalty methods in term of iteration numbers and better when comparing the values of the penalty parameter.