Abstract
Nondegeneracy conditions that guarantee that the optimal active constraints are identified in a finite number of iterations are studied. Results of this type have only been established for a few algorithms, and then under restrictive hypothesis. The main result is a characterization of those algorithms that identify the optimal constraints in a finite number of iterations. This result is obtained with a nondegeneracy assumption which is equivalent, in the standard nonlinear programming problem, to the assumption that there is a set of strictly complementary Lagrange multipliers. As an important consequence of the authors' results the way that this characterization applies to gradient projection and sequential quadratic programming algorithms is shown.
Keywords
MathematicsLagrange multiplierCharacterization (materials science)Finite setNonlinear programmingMathematical optimizationProjection (relational algebra)Quadratic equationQuadratic programmingSequential quadratic programmingNonlinear systemSet (abstract data type)Identification (biology)Applied mathematicsActive set methodAlgorithmMathematical analysisComputer science
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Publication Info
- Year
- 1988
- Type
- article
- Volume
- 25
- Issue
- 5
- Pages
- 1197-1211
- Citations
- 190
- Access
- Closed
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Cite This
James V. Burke,
Jorge J. Morè
(1988).
On the Identification of Active Constraints.
SIAM Journal on Numerical Analysis
, 25
(5)
, 1197-1211.
https://doi.org/10.1137/0725068
Identifiers
- DOI
- 10.1137/0725068