In this article we consider modiied search directions in the endgame of interior point methods for linear programming. In this stage, the normal equations determining the search directions become ill-conditioned. The modiied search directions are computed by solving perturbed systems in which the systems may be solved ef-ciently by the preconditioned conjugate gradient solver. We prove the conv...

In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact information (inexact non-linear operation programming). GAINLP was developed based on a GA-based inexact quadratic solving method. The Genetic Algorithm Solver of the Global Optimizatio...

The Inexact Restoration method for Euler discretization of state and control constrained optimal control problems is studied. Convergence of the discretized (finitedimensional optimization) problem to an approximate solution using the Inexact Restoration method and convergence of the approximate solution to a continuous-time solution of the original problem are established. It is proved that a ...

This paper investigates inexact Uzawa methods for nonlinear saddle point problems. We prove that the inexact Uzawa method converges globally and superlinearly even if the derivative of the nonlinear mapping does not exist. We show that the Newton-type decomposition method for saddle point problems is a special case of a Newton-Uzawa method. We discuss applications of inexact Uzawa methods to se...

We describe and critique the convergence properties of filterbased evolutionary pattern search algorithms (F-EPSAs). F-EPSAs implicitly use a filter to perform a multi-objective search for constrained problems such that convergence can be guaranteed. We provide two examples that illustrate how F-EPSAs may generate limit points other than constrained stationary points. F-EPSAs are evolutionary p...

This paper addresses the numerical solution of nonlinear eigenvector problems such as Gross–Pitaevskii and Kohn–Sham equation arising in computational physics chemistry. These characterize critical points energy minimization on infinite-dimensional Stiefel manifold. To efficiently compute minimizers, we propose a novel Riemannian gradient descent method induced by an energy-adaptive metric. Qua...