Practical methods of optimization; (2nd ed.)
Practical methods of optimization; (2nd ed.)
Preconditioners for indefinite systems arising in optimization
SIAM Journal on Matrix Analysis and Applications
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
On the Stability of Cholesky Factorization For Symmetric Quasidefinite Systems
SIAM Journal on Matrix Analysis and Applications
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
On the Newton interior-point method for nonlinear programming problems
Journal of Optimization Theory and Applications
Computational Optimization and Applications
Solving elliptic control problems with interior point and SQP methods: control and state constraints
Journal of Computational and Applied Mathematics - Special issue on SQP-based direct discretization methods for practical optimal control problems
Constraint Preconditioning for Indefinite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Computational Optimization and Applications
Methods for Solving Systems of Nonlinear Equations
Methods for Solving Systems of Nonlinear Equations
Computational Optimization and Applications
On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization
SIAM Journal on Scientific Computing
The Newton-arithmetic mean method for the solution of systems of nonlinear equations
Applied Mathematics and Computation
Inertia-controlling factorizations for optimization algorithms
Applied Numerical Mathematics
Parallel Computing - Special issue: Parallel computing in numerical optimization
Numerical solution of special linear and quadratic programs via a parallel interior-point method
Parallel Computing - Special issue: Parallel computing in numerical optimization
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioning Indefinite Systems in Interior Point Methods for Optimization
Computational Optimization and Applications
Some iterative methods for the solution of a symmetric indefinite KKT system
Computational Optimization and Applications
Non-negatively constrained image deblurring with an inexact interior point method
Journal of Computational and Applied Mathematics
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This paper deals with the solution of nonlinear programming problems arising from elliptic control problems by an interior point scheme. At each step of the scheme, we have to solve a large scale symmetric and indefinite system; inner iterative solvers, with an adaptive stopping rule, can be used in order to avoid unnecessary inner iterations, especially when the current outer iterate is far from the solution. In this work, we analyse the method of multipliers and the preconditioned conjugate gradient method as inner solvers for interior point schemes. We discuss the convergence of the whole approach, the implementation details and report the results of numerical experimentation on a set of large scale test problems arising from the discretization of elliptic control problems. A comparison with other interior point codes is also reported.