An interior-point trust-funnel algorithm for nonlinear optimization

An interior-point trust-funnel algorithm for nonlinear optimization

We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math. Prog., 122(1):155196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism...

A Trust Region Interior Point Algorithm for Linearly Constrained Optimization

We present an extension, for nonlinear optimization under linear constraints, of an algorithm for quadratic programming using a trust region idea introduced by Ye and Tse [Math. Programming, 44 (1989), pp. 157–179] and extended by Bonnans and Bouhtou [RAIRO Rech. Opér., 29 (1995), pp. 195–217]. Due to the nonlinearity of the cost, we use a linesearch in order to reduce the step if necessary. We...

A penalty-interior-point algorithm for nonlinear constrained optimization

Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization due ...

An Interior Point Algorithm for Solving Convex Quadratic Semidefinite Optimization Problems Using a New Kernel Function

In this paper, we consider convex quadratic semidefinite optimization problems and provide a primal-dual Interior Point Method (IPM) based on a new kernel function with a trigonometric barrier term. Iteration complexity of the algorithm is analyzed using some easy to check and mild conditions. Although our proposed kernel function is neither a Self-Regular (SR) fun...

Interior Point Methods for Nonlinear Optimization