Long-step strategies in interior-point primal-dual methods
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
A mathematical view of interior-point methods in convex optimization
A mathematical view of interior-point methods in convex optimization
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Lectures on modern convex optimization: analysis, algorithms, and engineering applications
Primal-Dual Interior-Point Methods for Self-Scaled Cones
SIAM Journal on Optimization
Convex Optimization
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In this paper we develop new primal-dual interior-point methods for linear programming problems, which are based on the concept of parabolic target space. We show that such schemes work in the infinity-neighborhood of the primal-dual central path. Nevertheless, these methods possess the best known complexity estimate. We demonstrate that the adaptive-step path-following strategies can be naturally incorporated in such schemes.