Linear Constraint
Enforce a mathematical relationship between numerical variables.
A linear constraint defines a weighted sum of variables that must satisfy a condition — like "components must add up to 100%".
How It Works
Select two or more numerical variables.
Assign a weight to each variable (the multiplier in the sum).
Choose an operator and a target value.
The constraint enforces: w1 x Var1 + w2 x Var2 + ... (operator) value
Operators
Operator | Meaning | You set |
Equal | Sum must equal exactly this value | A single target value |
Less than or equal | Sum must not exceed this value | An upper limit |
Greater than or equal | Sum must be at least this value | A lower limit |
Between | Sum must fall within a range | A lower and upper bound |
Examples
Mixture — Components must sum to 100%
Variables: Component A, Component B, Component C (each 0–100%)
Weights: all 1
Operator: Equal
Value: 100
This ensures: A + B + C = 100%. The optimizer will only suggest compositions that are valid mixtures.
Budget — Weighted cost limit
Variables: Reagent A (mL), Reagent B (mL)
Weights: 2 (cost per mL of A), 3 (cost per mL of B)
Operator: Less than or equal
Value: 500
This ensures: 2 x A + 3 x B ≤ 500. Total cost stays under budget.
Range — Bounded sum
Variables: Additive 1 (g), Additive 2 (g)
Weights: both 1
Operator: Between
Lower bound: 10, Upper bound: 50
This ensures: 10 ≤ Additive 1 + Additive 2 ≤ 50. Total additive loading stays in range.
When to Use It
Mixtures where components must sum to a total (e.g. 100%).
Budgets where a weighted total must not exceed a limit.
Physical limits like total volume, total weight, or total flow rate.
Good to Know
Linear constraints only work with numerical variables.
Weights can be any number (including decimals and negatives).
A weight of 1 means "add the variable value as-is." A weight of 2 means "double it."
Make sure the constraint is achievable given the variable bounds — an impossible constraint will prevent the optimizer from finding solutions.