Continuation methods for linear and quadratic programming
We present new finite dual methods for the Linear Programming (LP) and the Quadratic Programming (QP) problems. The dual of the LP problem with lower and upper bounds on the variables is formulated as an L1 minimization problem augmented with the addition of a linear term. Correspondingly, the dual of the QP problem is formulated as an L1 minimization problem augmented with the addition of a quadratic term. The augmented L1 problems are non-smooth. They are approximated by smooth problems depending on a positive parameter gamma. The smooth problems are solved by Newton iterations, and as gamma tends to zero the smooth solutions approximate the L1 solution. In fact the L1 solution and its dual can be detected for a positive (problem dependent) value of gamma, Therefore, the algorithms are finite. The LP method has been extensively tested, and encouraging results are reported for dense problems with up to 3500 variables. For the QP method preliminary results are presented.
- OSTI ID:
- 36250
- Report Number(s):
- CONF-9408161-; TRN: 94:009753-0575
- Resource Relation:
- Conference: 15. international symposium on mathematical programming, Ann Arbor, MI (United States), 15-19 Aug 1994; Other Information: PBD: 1994; Related Information: Is Part Of Mathematical programming: State of the art 1994; Birge, J.R.; Murty, K.G. [eds.]; PB: 312 p.
- Country of Publication:
- United States
- Language:
- English
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