A feasible SQP-GS algorithm for nonconvex, nonsmooth constrained optimization (Q393748)

An algorithm combining the gradient sampling (GS) technique with the sequential quadratic programming (SQP) method for nonconvex, nonsmooth constrained optimization problems with locally Lipschitz and continuously differentiable functions is presented. The proposed algorithm generates a sequence of feasible iterations and guarantees that the objective function is monotonically decreasing. It is an alternative of the penalty function based SQP-GS algorithm proposed by \textit{F. E. Curtis} and \textit{M. L. Overton} [SIAM J. Optim. 22, No. 2, 474--500 (2012; Zbl 1246.49031)]. Instead of the penalty function, serving as a merit function to generate the next iterate, the authors make use of the improvement function, which is one of the most effective tools to handle constraints and plays a significant role in global convergence analysis.