Ternary search¶

An interval-reduction search for the extremum of a unimodal function that compares two interior points and discards the third of the domain that cannot contain the optimum.

Version: v1 · 2026-09-08 · History
Domain-specific #: 7095
Origin domain: optimization algorithms
Subdomain: optimization algorithms

Core Idea¶

Ternary search exploits monotone rise then fall, or fall then rise, to shrink a continuous interval or discrete ordered domain without using derivatives. Two ordered probe points split the current interval into thirds; their function values and the declared unimodality orientation exclude an outer segment, and iteration continues to a tolerance or small discrete residue. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.

Scope of Application¶

Ternary search belongs to optimization algorithms and is useful where the analyst can specify the typed optimization algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, then evaluate the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity are explicit. The scope is broad within that domain but bounded by the need for the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity are explicit. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Clarity¶

The abstraction clarifies a crowded vocabulary by making the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Ternary search can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.

Manages Complexity¶

Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Ternary search. Ternary search compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.

Abstract Reasoning¶

Identify the carrier. State what the elements, states, objects, or observations are: the typed optimization algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity are explicit independently of one notation or implementation.

Knowledge Transfer¶

Knowledge transfers strongly among subfields of optimization algorithms because they reuse the typed optimization algorithms carrier, defining objects and relations, parameters, conventions, evidence, boundary cases, and comparison targets, Two ordered probe points split the current interval into thirds; their function values and the declared unimodality orientation exclude an outer segment, and iteration continues to a tolerance or small discrete residue., and type the carrier, state every parameter and convention in the definition, test that the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.

Relationships to Other Abstractions¶

Current abstraction Ternary search Domain-specific

Parents (1) — more general patterns this builds on

Ternary search is a kind of Algorithm Prime

The proposed strict upward parent is prime:algorithm.

Hierarchy paths (2) — routes to 2 parentless roots

Ternary search → Algorithm → Function (Mapping)

Show alternative path (1)

Neighborhood in Abstraction Space¶

Ternary search sits in a crowded region of the domain-specific corpus (28^th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

Family — Nonlinear & Simulation Optimization (7 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-09-08