A two-stage feasible directions algorithm for nonlinear constrained optimization
Mathematical Programming: Series A and B
SIAM Journal on Control and Optimization
An extension of Karmarkar's algorithm and the trust region method for quadratic programming
on Progress in Mathematical Programming: Interior-Point and Related Methods
An extension of Karmarkar projective algorithm for convex quadratic programming
Mathematical Programming: Series A and B
Interior path following primal-dual algorithms. Part II: Convex quadratic programming
Mathematical Programming: Series A and B
On affine scaling algorithms for nonconvex quadratic programming
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
On the complexity of approximating a KKT point of quadratic programming
Mathematical Programming: Series A and B
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Trust-region methods
Interior Methods for Nonlinear Optimization
SIAM Review
Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming
SIAM Journal on Optimization
Global Convergence of the Affine Scaling Algorithm for Convex Quadratic Programming
SIAM Journal on Optimization
A Trust Region Interior Point Algorithm for Linearly Constrained Optimization
SIAM Journal on Optimization
Primal-Dual Interior Methods for Nonconvex Nonlinear Programming
SIAM Journal on Optimization
A Barrier Function Method for the Nonconvex Quadratic Programming Problem with Box Constraints
Journal of Global Optimization
A Simple Primal-Dual Feasible Interior-Point Method for Nonlinear Programming with Monotone Descent
Computational Optimization and Applications
A Feasible Sequential Linear Equation Method for Inequality Constrained Optimization
SIAM Journal on Optimization
Interior algorithms for linear, quadratic, and linearly constrained convex programming
Interior algorithms for linear, quadratic, and linearly constrained convex programming
SIAM Journal on Optimization
Convergence Properties of Dikin"s Affine Scaling Algorithm for Nonconvex Quadratic Minimization
Journal of Global Optimization
A truncated-CG style method for symmetric generalized eigenvalue problems
Journal of Computational and Applied Mathematics
Optimization Methods & Software - Dedicated to Professor Michael J.D. Powell on the occasion of his 70th birthday
Fitting curves and surfaces to point clouds in the presence of obstacles
Computer Aided Geometric Design
Dataflow-based implementation of model predictive control
ACC'09 Proceedings of the 2009 conference on American Control Conference
Multi-Standard Quadratic Optimization: interior point methods and cone programming reformulation
Computational Optimization and Applications
Adaptive constraint reduction for convex quadratic programming
Computational Optimization and Applications
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Two interior-point algorithms are proposed and analyzed, for the (local) solution of (possibly) indefinite quadratic programming problems. They are of the Newton-KKT variety in that (much like in the case of primal-dual algorithms for linear programming) search directions for the "primal" variables and the Karush-Kuhn-Tucker (KKT) multiplier estimates are components of the Newton (or quasi-Newton) direction for the solution of the equalities in the first-order KKT conditions of optimality or a perturbed version of these conditions. Our algorithms are adapted from previously proposed algorithms for convex quadratic programming and general nonlinear programming. First, inspired by recent work by P. Tseng based on a "primal" affine-scaling algorithm (à la Dikin) [J. of Global Optimization, 30 (2004), no. 2, 285---300], we consider a simple Newton-KKT affine-scaling algorithm. Then, a "barrier" version of the same algorithm is considered, which reduces to the affine-scaling version when the barrier parameter is set to zero at every iteration, rather than to the prescribed value. Global and local quadratic convergence are proved under nondegeneracy assumptions for both algorithms. Numerical results on randomly generated problems suggest that the proposed algorithms may be of great practical interest.