Ghost Penalties in Nonconvex Constrained Optimization: Diminishing Stepsizes and Iteration Complexity

We consider nonconvex constrained optimization problems and propose a new approach to the convergence analysis based on penalty functions. make use of classical functions in an unconventional way, that only enter theoretical while algorithm itself is free. Based this idea, we are able establish several results, including first general for diminishing stepsize methods nonconvex, optimization, showing generalized stationary points, complexity study sequential quadratic programming–type algorithms.