Local Convergence of the Affine-Scaling Interior-Point Algorithm for Nonlinear Programming
Computational Optimization and Applications
Primal-dual Newton-type interior-point method for topology optimization
Journal of Optimization Theory and Applications
Local Convergence of a Primal-Dual Method for Degenerate Nonlinear Programming
Computational Optimization and Applications
A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent
Computational Optimization and Applications
Topology Optimization of Conductive Media Described by Maxwell's Equations
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Inertia-controlling factorizations for optimization algorithms
Applied Numerical Mathematics
Feasible Interior Methods Using Slacks for Nonlinear Optimization
Computational Optimization and Applications
Newton-KKT interior-point methods for indefinite quadratic programming
Computational Optimization and Applications
Computational Optimization and Applications
Research article: Assessing a multiple QTL search using the variance component model
Computational Biology and Chemistry
A truncated Newton method in an augmented Lagrangian framework for nonlinear programming
Computational Optimization and Applications
Primal-dual interior-point method for thermodynamic gas-particle partitioning
Computational Optimization and Applications
A primal-dual augmented Lagrangian
Computational Optimization and Applications
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This paper concerns large-scale general (nonconvex) nonlinear programming when first and second derivatives of the objective and constraint functions are available. A method is proposed that is based on finding an approximate solution of a sequence of unconstrained subproblems parameterized by a scalar parameter. The objective function of each unconstrained subproblem is an augmented penalty-barrier function that involves both primal and dual variables. Each subproblem is solved with a modified Newton method that generates search directions from a primal-dual system similar to that proposed for interior methods. The augmented penalty-barrier function may be interpreted as a merit function for values of the primal and dual variables.An inertia-controlling symmetric indefinite factorization is used to provide descent directions and directions of negative curvature for the augmented penalty-barrier merit function. A method suitable for large problems can be obtained by providing a version of this factorization that will treat large sparse indefinite systems.