A non-monotone Inexact Restoration approach for minimization with orthogonality constraints

In this work we consider the problem of minimizing a differentiable functional restricted to the set of $n\times p$ matrices with orthonormal columns. This problem appears in several fields such as statistics, signal processing, global positioning system, machine learning, physics, chemistry and others. We present an algorithm based on a recent non-monotone variation of the … Read more

Non-monotone Inexact Restoration Method for nonlinear programming

This paper deals with a new variant of the Inexact Restoration Method of Fischer and Friedlander (COAP, 46, pp. 333-346, 2010). We propose an algorithm that replaces the monotone line-search performed in the tangent phase (with regard to the penalty function) by a non-monotone one. Con- vergence to feasible points satisfying the approximate gradient projection … Read more

Density-based Globally Convergent Trust-Region Methods for Self-Consistent Field Electronic Structure Calculations

A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more