6533b86cfe1ef96bd12c7f80
RESEARCH PRODUCT
Hoffman's Error Bound, Local Controllability, and Sensitivity Analysis
Abderrahim Jouranisubject
Discrete mathematicsMaxima and minimaControllabilityLinear inequalityControl and OptimizationApplied MathematicsErgodicityVariational inequalityApplied mathematicsConstant (mathematics)Farkas' lemmaImplicit function theoremMathematicsdescription
Our aim is to present sufficient conditions ensuring Hoffman's error bound for lower semicontinuous nonconvex inequality systems and to analyze its impact on the local controllability, implicit function theorem for (non-Lipschitz) multivalued mappings, generalized equations (variational inequalities), and sensitivity analysis and on other problems like Lipschitzian properties of polyhedral multivalued mappings as well as weak sharp minima or linear conditioning. We show how the information about our sufficient conditions can be used to provide a computable constant such that Hoffman's error bound holds. We also show that this error bound is nothing but the classical Farkas lemma for linear inequality systems. In the latter case our constant may be computed explicitly.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2000-01-01 | SIAM Journal on Control and Optimization |