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Tropical optimization
§Tropical Optimization
This module implements optimization algorithms in tropical semirings and max-plus algebra, leveraging the tropical arithmetic from the amari-tropical crate.
§Mathematical Background
Tropical optimization operates in the tropical semiring (ℝ ∪ {-∞}, ⊕, ⊗) where:
- Tropical addition: a ⊕ b = max(a, b)
- Tropical multiplication: a ⊗ b = a + b
- Tropical zero: -∞
- Tropical one: 0
This algebra is particularly useful for:
- Shortest path problems
- Scheduling optimization
- Resource allocation
- Dynamic programming
- Discrete event systems
§Key Algorithms
- Tropical Linear Programming: Solve Ax ⊕ b = c in tropical algebra
- Tropical Convex Optimization: Minimize tropical convex functions
- Max-Plus Dynamic Programming: Solve optimal control problems
- Tropical Eigenvalue Problems: Find tropical eigenvalues and eigenvectors
- Scheduling Optimization: Optimize event timing in discrete systems
Modules§
- scheduling
- Scheduling optimization using tropical algebra
Structs§
- Tropical
Config - Configuration for tropical optimization algorithms
- Tropical
Optimizer - Tropical optimization solver
- Tropical
Result - Results from tropical optimization
Traits§
- Tropical
Constraint - Trait for tropical constraint functions
- Tropical
Objective - Trait for tropical objective functions