On the iterative solution of KKT systems in potential reduction software for large-scale quadratic problems

Authors:
S. Cafieri;M. D'Apuzzo;V. Simone;D. Serafino
Affiliations:
Department of Mathematics, Second University of Naples, Caserta, Italy I-81100;Department of Mathematics, Second University of Naples, Caserta, Italy I-81100;Department of Mathematics, Second University of Naples, Caserta, Italy I-81100;Department of Mathematics, Second University of Naples, Caserta, Italy I-81100
Venue:
Computational Optimization and Applications
Year:
2007

Citing 25
Cited 2

A new polynomial-time algorithm for linear programming

Combinatorica
On projected Newton barrier methods for linear programming and an equivalence to Karmarkar's projective method

Mathematical Programming: Series A and B
A centered projective algorithm for linear programming

Mathematics of Operations Research
An OnL iteration potential reduction algorithm for linear complementary problems

Mathematical Programming: Series A and B
Path-following methods for linear programming

SIAM Review
Preconditioners for indefinite systems arising in optimization

SIAM Journal on Matrix Analysis and Applications
Computational results of an interior point algorithm for large scale linear programming

Mathematical Programming: Series A and B - Special issue on interior point methods for linear programming: theory and practice
An interior point method for quadratic programs based on conjugate projected gradients

Computational Optimization and Applications
Stability of Symmetric Ill-Conditioned Systems Arising in Interior Methods for Constrained Optimization

SIAM Journal on Matrix Analysis and Applications
Potential-reduction methods in mathematical programming

Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Stability of Augmented System Factorizations in Interior-Point Methods

SIAM Journal on Matrix Analysis and Applications
Primal-dual interior-point methods

Primal-dual interior-point methods
Interior point algorithms: theory and analysis

Interior point algorithms: theory and analysis
An Iteration for Indefinite Systems and Its Application to the Navier--Stokes Equations

SIAM Journal on Scientific Computing
Constraint Preconditioning for Indefinite Linear Systems

SIAM Journal on Matrix Analysis and Applications
The Multifrontal Solution of Indefinite Sparse Symmetric Linear

ACM Transactions on Mathematical Software (TOMS)
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization

SIAM Journal on Scientific Computing
Krylov Subspace Methods for Saddle Point Problems with Indefinite Preconditioning

SIAM Journal on Matrix Analysis and Applications
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming

SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming

SIAM Journal on Optimization
A Computational Study of the Homogeneous Algorithm for Large-scale Convex Optimization

Computational Optimization and Applications
Object-oriented software for quadratic programming

ACM Transactions on Mathematical Software (TOMS)
Parallel computational issues of an interior point method for solving large bound-constrained quadratic programming problems

Parallel Computing - Special issue: Parallel computing in numerical optimization
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited

ACM Transactions on Mathematical Software (TOMS)
Preconditioning Indefinite Systems in Interior Point Methods for Optimization

Computational Optimization and Applications

Stopping criteria for inner iterations in inexact potential reduction methods: a computational study

Computational Optimization and Applications
On mutual impact of numerical linear algebra and large-scale optimization with focus on interior point methods

Computational Optimization and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

Iterative solvers appear to be very promising in the development of efficient software, based on Interior Point methods, for large-scale nonlinear optimization problems. In this paper we focus on the use of preconditioned iterative techniques to solve the KKT system arising at each iteration of a Potential Reduction method for convex Quadratic Programming. We consider the augmented system approach and analyze the behaviour of the Constraint Preconditioner with the Conjugate Gradient algorithm. Comparisons with a direct solution of the augmented system and with MOSEK show the effectiveness of the iterative approach on large-scale sparse problems.