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Amenable cones: error bounds without constraint qualifications
- Source :
- Mathematical Programming. 186:1-48
- Publication Year :
- 2019
- Publisher :
- Springer Science and Business Media LLC, 2019.
-
Abstract
- We provide a framework for obtaining error bounds for linear conic problems without assuming constraint qualifications or regularity conditions. The key aspects of our approach are the notions of amenable cones and facial residual functions. For amenable cones, it is shown that error bounds can be expressed as a composition of facial residual functions. The number of compositions is related to the facial reduction technique and the singularity degree of the problem. In particular, we show that symmetric cones are amenable and compute facial residual functions. From that, we are able to furnish a new H\"olderian error bound, thus extending and shedding new light on an earlier result by Sturm on semidefinite matrices. We also provide error bounds for the intersection of amenable cones, this will be used to provided error bounds for the doubly nonnegative cone.<br />Comment: 36 pages, 1 figure. This version was significantly revised. A discussion on the relation between amenability and related concepts was added. In particular, there is a proof that amenable cones are nice and, therefore, facially exposed. Also, gathered the results on symmetric cones in a single section. Several typos and minor issues were fixed
- Subjects :
- General Mathematics
ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION
MathematicsofComputing_NUMERICALANALYSIS
0211 other engineering and technologies
010103 numerical & computational mathematics
02 engineering and technology
Residual
01 natural sciences
Reduction (complexity)
Singularity
Intersection
ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION
FOS: Mathematics
Mathematics - Numerical Analysis
0101 mathematics
Mathematics - Optimization and Control
ComputingMethodologies_COMPUTERGRAPHICS
Mathematics
Discrete mathematics
021103 operations research
Degree (graph theory)
Numerical analysis
Numerical Analysis (math.NA)
Constraint (information theory)
Optimization and Control (math.OC)
Conic section
90C25, 90C46, 90C31
Software
Subjects
Details
- ISSN :
- 14364646 and 00255610
- Volume :
- 186
- Database :
- OpenAIRE
- Journal :
- Mathematical Programming
- Accession number :
- edsair.doi.dedup.....ad6db038a3f940a921f91071a5530c44