Interior-point ℓ
2-penalty methods for nonlinear programming with strong global convergence properties |
| |
Authors: | L Chen D Goldfarb |
| |
Institution: | (1) IEOR Department, Columbia University, New York, NY 10027, USA |
| |
Abstract: | We propose two line search primal-dual interior-point methods for nonlinear programming that approximately solve a sequence
of equality constrained barrier subproblems. To solve each subproblem, our methods apply a modified Newton method and use
an ℓ2-exact penalty function to attain feasibility. Our methods have strong global convergence properties under standard assumptions.
Specifically, if the penalty parameter remains bounded, any limit point of the iterate sequence is either a Karush-Kuhn-Tucker
(KKT) point of the barrier subproblem, or a Fritz-John (FJ) point of the original problem that fails to satisfy the Mangasarian-Fromovitz
constraint qualification (MFCQ); if the penalty parameter tends to infinity, there is a limit point that is either an infeasible
FJ point of the inequality constrained feasibility problem (an infeasible stationary point of the infeasibility measure if
slack variables are added) or a FJ point of the original problem at which the MFCQ fails to hold. Numerical results are given
that illustrate these outcomes.
Research supported by the Presidential Fellowship of Columbia University.
Research supported in part by NSF Grant DMS 01-04282, DOE Grant DE-FG02-92EQ25126 and DNR Grant N00014-03-0514. |
| |
Keywords: | Constrained optimization nonlinear programming primal-dual interior-point method global convergence penalty-barrier method modified Newton method |
本文献已被 SpringerLink 等数据库收录! |
|