Local Convergence of the Affine-Scaling Interior-Point Algorithm for Nonlinear Programming

Authors:
L. N. Vicente
Affiliations:
Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal. lvicente@mat.uc.pt
Venue:
Computational Optimization and Applications
Year:
2000

Citing 13
Cited 3

A new polynomial-time algorithm for linear programming

Combinatorica
The projective SUMT method for convex programming

Mathematics of Operations Research
Interior point methods for optimal control of discrete time systems

Journal of Optimization Theory and Applications
On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

Mathematical Programming: Series A and B
On the formulation and theory of the Newton interior-point method for nonlinear programming

Journal of Optimization Theory and Applications
Superlinear and quadratic convergence of some primal—dual interior point methods for constrained optimization

Mathematical Programming: Series A and B
Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming Problems

SIAM Journal on Control and Optimization
An Interior-Point Algorithm for Nonconvex Nonlinear Programming

Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems

SIAM Journal on Scientific Computing
Superlinear Convergence of Affine-Scaling Interior-Point Newton Methods for Infinite-Dimensional Nonlinear Problems with Pointwise Bounds

SIAM Journal on Control and Optimization
Primal-Dual Interior Methods for Nonconvex Nonlinear Programming

SIAM Journal on Optimization
A Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization

A Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization
AN INTERIOR POINT ALGORITHM FOR THE GENERAL NONLINEAR PROGRAMMING PROBLEM WITH TRUST REGION GLOBALIZATION

AN INTERIOR POINT ALGORITHM FOR THE GENERAL NONLINEAR PROGRAMMING PROBLEM WITH TRUST REGION GLOBALIZATION

Comparison of two sets of first-order conditions as bases of interior-point Newton methods for optimization with simple bounds

Journal of Optimization Theory and Applications
Local Convergence of a Primal-Dual Method for Degenerate Nonlinear Programming

Computational Optimization and Applications
Local analysis of the feasible primal-dual interior-point method

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper addresses the local convergence properties of the affine-scaling interior-point algorithm for nonlinear programming. The analysis of local convergence is developed in terms of parameters that control the interior-point scheme and the size of the residual of the linear system that provides the step direction. The analysis follows the classical theory for quasi-Newton methods and addresses q-linear, q-superlinear, and q-quadratic rates of convergence.