We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters $\mu$ converging to zero. We prove that it converges q-superlinearly for each fixed $\mu$. We also show that it is globally convergent to the analytic center of the primal-dual optimal set when $\mu$ tends to 0 and strict complementarity holds.
Publié le : 2000-07-04
Classification:
superlinear convergence,
primal-dual method,
interior point algorithm,
line-search,
analytic center,
BFGS quasi-Newton approximations,
constrained optimization,
convex programming,
[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
@article{hal-00955220,
author = {Armand, Paul and Gilbert, Jean Charles and Jan, Sophie},
title = {A feasible BFGS interior point algorithm for solving convex minimization problems},
journal = {HAL},
volume = {2000},
number = {0},
year = {2000},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00955220}
}
Armand, Paul; Gilbert, Jean Charles; Jan, Sophie. A feasible BFGS interior point algorithm for solving convex minimization problems. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00955220/