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Mathematical Notation

Naming Conventions

FlixOpt uses the following naming conventions:

  • All optimization variables are denoted by italic letters (e.g., \(x\), \(y\), \(z\))
  • All parameters and constants are denoted by non italic small letters (e.g., \(\text{a}\), \(\text{b}\), \(\text{c}\))
  • All Sets are denoted by greek capital letters (e.g., \(\mathcal{F}\), \(\mathcal{E}\))
  • All units of a set are denoted by greek small letters (e.g., \(\mathcal{f}\), \(\mathcal{e}\))
  • The letter \(i\) is used to denote an index (e.g., \(i=1,\dots,\text n\))
  • All time steps are denoted by the letter \(\text{t}\) (e.g., \(\text{t}_0\), \(\text{t}_1\), \(\text{t}_i\))

Timesteps

Time steps are defined as a sequence of discrete time steps \(\text{t}_i \in \mathcal{T} \quad \text{for} \quad i \in \{1, 2, \dots, \text{n}\}\) (left-aligned in its timespan). From this sequence, the corresponding time intervals \(\Delta \text{t}_i \in \Delta \mathcal{T}\) are derived as

\[\Delta \text{t}_i = \text{t}_{i+1} - \text{t}_i \quad \text{for} \quad i \in \{1, 2, \dots, \text{n}-1\}\]

The final time interval \(\Delta \text{t}_\text n\) defaults to \(\Delta \text{t}_\text n = \Delta \text{t}_{\text n-1}\), but is of course customizable. Non-equidistant time steps are also supported.