pith. sign in
inductive

OptimizationClass

definition
show as:
module
IndisputableMonolith.Mathematics.OptimizationProblemClassesFromConfigDim
domain
Mathematics
line
15 · github
papers citing
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plain-language theorem explainer

OptimizationClass enumerates the five canonical optimization problem types that arise when configuration dimension is fixed at five. Operations researchers and systems theorists cite the enumeration when classifying decision problems by structure and computational character. The declaration is a direct inductive construction that derives decidable equality, representation, and finite-type instances automatically.

Claim. The optimization problem classes comprise linear programs, convex nonlinear programs, integer programs, stochastic programs, and dynamic programs.

background

The module defines five canonical optimization classes tied to configuration dimension five. These classes are linear, convex nonlinear, integer, stochastic, and dynamic. The local theoretical setting treats the enumeration as exhaustive for the Recognition Science mathematical layer, with no additional axioms or hypotheses required.

proof idea

Direct inductive definition introducing five constructors. Derived instances for DecidableEq, Repr, BEq, and Fintype are generated by Lean without explicit proof steps.

why it matters

The definition supplies the finite set whose cardinality is certified by the downstream theorem optimizationClass_count and the structure OptimizationClassesCert. It realizes the module claim that configuration dimension equals five. In the Recognition Science framework it anchors the operations-research classification layer to the fixed dimension without introducing new constants or forcing steps.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.