Mathematical specification

These pages provide comprehensive description of the variables and equations in the core MESSAGEix mathematical implementation.

• Sets and mappings definition
  • Sets in the MESSAGEix implementation
  • Category types and mappings
  • Mappings sets
  • Mapping sets (flags) for bounds
  • Mapping sets (flags) for fixed variables
• Parameter definition
  • General parameters of the MESSAGEix implementation
  • Parameters of the Resources section
  • Parameters of the Demand section
  • Parameters of the Technology section
  • Parameters of the Emission section
  • Parameters of the Land-Use model emulator section
  • Parameters of the Share Constraints section
  • Parameters of the Relations section
  • Fixed variable values
• Mathematical formulation (core model)
  • Notation declaration
  • Objective function
  • Regional system cost accounting function
  • Resource and commodity section
  • Technology section
  • System reliability and flexibility requirements
  • Constraints on shares of technologies and commodities
  • Emission section
  • Land-use model emulator section
  • Section of generic relations (linear constraints)
• Solve statement workflow
  • Perfect-foresight model
  • Recursive-dynamic and myopic model
• Standard output reports
• Auxiliary investment parameters
  • Levelized capital costs
  • Construction time accounting
  • Investment costs beyond the model horizon
  • Remaining installed capacity
• MACRO - Mathematical formulation
  • Notation declaration
  • Decision variables