We consider the problem of minimizing a sum of a convex function and a composition of a convex function with a smooth map. Important examples include exact penalty formulations of nonlinear programs and nonlinear least squares problems with side constraints. The basic algorithm we rely on is the well-known prox-linear method, which in each iteration … Read more
The Levenberg-Marquardt algorithm is one of the most popular algorithms for the solution of nonlinear least squares problems. Motivated by the problem structure in data assimilation, we consider in this paper the extension of the classical Levenberg-Marquardt algorithm to the scenarios where the linearized least squares subproblems are solved inexactly and/or the gradient model is … Read more
In the context of convex mixed-integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective NLP subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness … Read more
In the context of convex mixed-integer nonlinear programming (MINLP), we investigate how the outer approximation method and the generalized Benders decomposition method are affected when the respective NLP subproblems are solved inexactly. We show that the cuts in the corresponding master problems can be changed to incorporate the inexact residuals, still rendering equivalence and finiteness … Read more