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Méthodes de Points Intérieurs et de quasi-Newton

Abstract : This thesis is interested in interior point and quasi-Newton methods in Nonlinear Optimization and with their implementation. One presents the code NOPTIQ using the limited memory BFGS formulas to solve large scale problems. The originality of this approach is the use of these formulas within the framework of interior point methods. The storage requirement and the computing cost of one iteration are then low. One shows that NOPTIQ is robust and its performance are comparable with the reference codes l-BFGS-B and LANCELOT. One presents also an infeasible algorithm using the preceding methods to solve a nonlinear problem with inequality constraints and linear equality constraints. The idea is to penalize the problem using shift variables and a variant of the big-M method of linear programming. The q-superlinear convergence of the inner iterates and the global convergence of outer iterates are shown.
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Contributor : Philippe Segalat <>
Submitted on : Monday, March 29, 2004 - 11:09:18 AM
Last modification on : Thursday, January 11, 2018 - 6:12:25 AM
Long-term archiving on: : Friday, April 2, 2010 - 9:01:36 PM


  • HAL Id : tel-00005478, version 1



Philippe Segalat. Méthodes de Points Intérieurs et de quasi-Newton. Mathématiques [math]. Université de Limoges, 2002. Français. ⟨tel-00005478⟩



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