feasible method – Optimization Online

A New First-order Algorithmic Framework for Optimization Problems with Orthogonality Constraints

Published: 2016/09/30, Updated: 2017/10/10

Basic Sciences Applications, Constrained Nonlinear Optimization block-coordinate descent, feasible method, householder transformation, orthogonality constraint, stiefel manifold, trust-region methods

In this paper, we consider a class of optimization problems with orthogonality constraints, the feasible region of which is called the Stiefel manifold. Our new framework combines a function value reduction step with a correction step. Different from the existing approaches, the function value reduction step of our algorithmic framework searches along the standard Euclidean … Read more

Feasible Interior Methods Using Slacks for Nonlinear Optimization

Published: 2001/02/12

Richard H. Byrd

Richard A. Waltz

Jorge Nocedal

Constrained Nonlinear Optimization barrier method, constrained optimization, feasible method, interior point methods, large-scale optimization, nonlinear programming, primal-dual algorithms, sequential quadratic programming, trust-region methods

A slack-based feasible interior point method is described which can be derived as a modification of infeasible methods. The modification is minor for most line search methods, but trust region methods require special attention. It is shown how the Cauchy point, which is often computed in trust region methods, must be modified so that the … Read more