A two-stage feasible directions algorithm for nonlinear constrained optimization
Mathematical Programming: Series A and B
A tool for the analysis of Quasi-Newton methods with application to unconstrained minimization
SIAM Journal on Numerical Analysis
Primal-dual interior-point methods
Primal-dual interior-point methods
On the Existence and Convergence of the Central Path for Convex Programming and Some Duality Results
Computational Optimization and Applications
A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems
SIAM Journal on Optimization
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We describe an infeasible interior point algorithm for convex minimization problems. The method uses quasi-Newton techniques for approximating the second derivatives and providing superlinear convergence. We propose a new feasibility control of the iterates by introducing shift variables and by penalizing them in the barrier problem. We prove global convergence under standard conditions on the problem data, without any assumption on the behavior of the algorithm.