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

Local path-following property of inexact interior methods in nonlinear programming

We study the local behavior of a primal-dual inexact interior point methods for solving nonlinear systems arising from the solution of nonlinear optimization problems or more generally from nonlinear complementarity problems. The algorithm is based on the Newton method applied to a sequence of perturbed systems that follows by perturbation of the complementarity equations of … Read more

Chebyshev approximation of the null function by an affine combination of complex exponential functions

We describe the theoretical solution of an approximation problem that uses a finite weighted sum of complex exponential functions. The problem arises in an optimization model for the design of a telescopes array occurring within optical interferometry for direct imaging in astronomy. The problem is to find the optimal weights and the optimal positions of … Read more

A local convergence property of primal-dual methods for nonlinear programming

We prove a new local convergence property of a primal-dual method for solving nonlinear optimization problem. Following a standard interior point approach, the complementarity conditions of the original primal-dual system are perturbed by a parameter which is driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed … Read more

Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and … Read more