Slater’s condition
E1044001
Slater’s condition is a regularity condition in convex optimization that guarantees strong duality and the validity of the Karush–Kuhn–Tucker optimality conditions by requiring the existence of a strictly feasible point.
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
constraint qualification
ⓘ
duality condition ⓘ regularity condition ⓘ |
| appliesTo |
constrained optimization problems
ⓘ
convex optimization problems ⓘ |
| assumes |
affine equality constraints
ⓘ
convex inequality constraint functions ⓘ convex objective function ⓘ |
| category |
convex analysis concept
ⓘ
optimization theory concept ⓘ |
| ensures |
existence of optimal Lagrange multipliers
ⓘ
strong duality ⓘ validity of Karush–Kuhn–Tucker conditions ⓘ zero duality gap ⓘ |
| field |
convex optimization
ⓘ
mathematical optimization ⓘ |
| holdsFor | convex problems with nonempty interior of feasible set ⓘ |
| isNotNecessaryFor | strong duality in all convex problems ⓘ |
| isSufficientFor | strong duality in convex programs ⓘ |
| namedAfter | Morton L. Slater NERFINISHED ⓘ |
| relatesTo |
Karush–Kuhn–Tucker conditions
NERFINISHED
ⓘ
Lagrange dual problem ⓘ constraint qualifications in nonlinear programming ⓘ |
| requires |
existence of a strictly feasible point
ⓘ
interior point satisfying inequality constraints strictly ⓘ |
| typicalFormulation | there exists x such that all inequality constraints are strictly satisfied and equality constraints are satisfied ⓘ |
| usedIn |
Lagrangian duality theory
NERFINISHED
ⓘ
analysis of dual problems ⓘ derivation of KKT optimality conditions ⓘ interior-point methods theory ⓘ |
Referenced by (1)
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