A penalty-function-free line search SQP method for nonlinear programming
The following optimization problem is considered: \[ \text{Minimize }f(x) \text{ subject to }c_i(x)=0,\;i=1,\dots,p,\;c_i(x)\leq 0,\;i=p+1, \dots,m, \] where \(f:\mathbb R^n\to \mathbb R\), \(c_i:\mathbb R^n\to \mathbb R\), \(i=1,\dots,m\) are twice continuously differentiable functions. The authors propose a special sequential quadratic programming (SQP) method for solving the problem. The key point of the concept is that the trial point generated by solving a trust region SQP problem is accepted if there is a sufficient decrease of the objective function or the constraint violation. No penalty parameter needs to be chosen and no filter is used. The proposed method is a non-monotone line search SQP method, which interprets the optimization problem as a bi-objective optimization problem. Local and global convergence of the proposed method is investigated and it is shown that under certain additional conditions the method converges superlinearly. Some numerical results and experiments are reported in the concluding part of the paper.
scientific article; zbMATH DE number 5559058