A primal-dual modified log-barrier method for inequality constrained nonlinear optimization

We present a primal-dual modified log-barrier algorithm to solve inequality constrained nonlinear optimization problems. Basically, the algorithm is a Newton-like method applied to a perturbation of the optimality system that follows from a reformulation of the initial problem by introducing a modified log-barrier function to handle inequality constraints. The algorithm uses an outer/inner iteration scheme … Read more

Trust-Region Algorithms for Training Responses: Machine Learning Methods Using Indefinite Hessian Approximations

Machine learning (ML) problems are often posed as highly nonlinear and nonconvex unconstrained optimization problems. Methods for solving ML problems based on stochastic gradient descent are easily scaled for very large problems but may involve fine-tuning many hyper-parameters. Quasi-Newton approaches based on the limited-memory Broyden-Fletcher-Goldfarb-Shanno (BFGS) update typically do not require manually tuning hyper-parameters but … Read more

Branch and Bound based methods to minimize the energy consumed by an electrical vehicle on long travels with slopes

We consider the problem of minimization of the energy consumed by an electrical vehicle performing quite long travels with slopes. The model we address here, takes into account the electrical and mechanical differential equations of the vehicle. This yields a mixed-integer optimal control problem that can be approximated, using a methodology based on some decomposition … Read more

Study of a primal-dual algorithm for equality constrained minimization

The paper proposes a primal-dual algorithm for solving an equality constrained minimization problem. The algorithm is a Newton-like method applied to a sequence of perturbed optimality systems that follow naturally from the quadratic penalty approach. This work is first motivated by the fact that a primal-dual formulation of the quadratic penalty provides a better framework … Read more