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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Slater’s condition canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13509476 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Slater’s condition Context triple: [KKT conditions, relatedConcept, Slater’s condition]
-
A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
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B.
KKT conditions
KKT conditions are a set of necessary (and under certain conditions, sufficient) optimality conditions used in nonlinear programming to characterize solutions of constrained optimization problems.
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C.
Convex Optimization
Convex Optimization is a widely used graduate-level textbook that systematically develops the theory, algorithms, and applications of convex optimization problems in engineering, statistics, and applied mathematics.
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D.
Kantorovich duality
Kantorovich duality is a fundamental result in optimal transport theory that characterizes the optimal transport cost as the supremum of a dual variational problem over suitable test functions.
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E.
Lagrange multipliers
Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Slater’s condition Target entity description: 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.
-
A.
Karush–Kuhn–Tucker conditions
The Karush–Kuhn–Tucker conditions are fundamental optimality criteria in nonlinear programming that generalize Lagrange multipliers to handle inequality constraints.
-
B.
KKT conditions
KKT conditions are a set of necessary (and under certain conditions, sufficient) optimality conditions used in nonlinear programming to characterize solutions of constrained optimization problems.
-
C.
Convex Optimization
Convex Optimization is a widely used graduate-level textbook that systematically develops the theory, algorithms, and applications of convex optimization problems in engineering, statistics, and applied mathematics.
-
D.
Kantorovich duality
Kantorovich duality is a fundamental result in optimal transport theory that characterizes the optimal transport cost as the supremum of a dual variational problem over suitable test functions.
-
E.
Lagrange multipliers
Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
- F. None of above. chosen
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Slater’s condition Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.