Parameters, variables, constraints and the objective

These four blocks carry the math. Each takes an optional description:, free text that the typeset legend prints.

parameters

A parameter declares a shape. The numbers arrive by name with the data.

dimensions:
  snapshot: { dtype: int }
parameters:
  load:
    dims: [snapshot]
  discount_rate:
    dims: [] # a scalar

Field
dims	required. The dimensions it is indexed by. [] means a scalar
dtype	float, int, bool, str	default float
description	free text	default null

The column has to match the dtype:

declared	the column
float	a float column, or an integer one
int	an integer column
bool	a boolean column	1 and 0 are not booleans. Cast the column
str	a string column

Only float and int are values. A str parameter is a label and a bool parameter is a mask: each selects rows in a where, and writing either as a coefficient, a term or a divisor is a load error. A 0 or 1 that is meant to be multiplied by is declared dtype: int.

variables

A variable is what the solver decides. There is one column per coordinate of dims.

dimensions:
  snapshot: { dtype: int }
  generator: { dtype: str }
parameters:
  capacity: { dims: [generator] }
variables:
  dispatch:
    dims: [snapshot, generator]
    where: "capacity > 0"
    bounds:
      lower: 0
      upper: capacity

Field
dims	required. The dimensions it is indexed by
where	which coordinates exist (absence)	default null
bounds.lower / bounds.upper	a finite number, or the name of a float or int parameter. null leaves that side open	default null
domain	continuous, integer or binary. binary carries fixed 0/1 bounds	default continuous
absence	undefined or zero: what a masked-out coordinate means (absence)	default undefined
description	free text	default null

An open side is null. A bound is never infinite: .inf and -.inf are refused, with null named as the rewrite.

A bound is a name or a number: upper: capacity is accepted, and upper: -rating is refused. Ship the negated column as data.

Equal bounds pin a variable (fix a quantity). A pinned variable is still a variable.

constraints

One block is one rule. The name of the block is the name of the constraint.

dimensions:
  snapshot: { dtype: int }
  generator: { dtype: str }
parameters:
  load: { dims: [snapshot] }
variables:
  dispatch: { dims: [snapshot, generator] }
constraints:
  power_balance:
    dims: [snapshot]
    expression: sum(dispatch, over=generator) == load

Field
dims	required. The rows this rule builds
expression	required. It uses exactly one of <=, >= or ==
where	which rows are built (absence)	default null
description	free text	default null

The dimensions of the expression must equal its dims (how dimensions combine).

At least one side of the comparator carries a variable. A comparison between numbers and parameters alone is refused at load.

dims: [] gives one scalar row. A scalar variable may not carry a where; put the condition on the constraints that use it.

Two regimes of one rule are two blocks, each under its own where: (state a rule that differs by regime).

objective

The objective is a single block with no name.

dimensions:
  generator: { dtype: str }
parameters:
  cost: { dims: [generator] }
variables:
  dispatch: { dims: [generator] }
objective:
  sense: minimize
  expression: sum(dispatch * cost)

Field
expression	required. Arithmetic, with no comparator
sense	minimize or maximize	default minimize
description	free text	default null

The expression must be scalar. Nothing is summed for you: sum(x * a) + sum(y * b) and sum(x * a + y * b) are both allowed, and they are different models.

There is one objective block. To pursue several goals, weight them into one expression.