Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
A strictly convex function on a Euclidean convex set has at most one global minimizer
Statement
A strictly convex real-valued function on a Euclidean convex set has at most one global minimizer. This asserts uniqueness only, not existence, and includes empty and singleton domains.
Facts & Assumptions
Given: A strictly convex function on a convex domain.
Strict convexity means that the convexity inequality is strict for distinct and (Convex and strictly convex functions on Euclidean convex sets).
Proof
Suppose distinct were both global minimizers with value . By [F1] at their midpoint, contradicting minimality.
Therefore two distinct global minimizers cannot exist. Empty and singleton domains satisfy the conclusion automatically.
Depends on
Used by
Nothing in the library uses this result yet.
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- S. Boyd and L. Vandenberghe, Convex Optimization, §3.1 (standard reference, not scraped)