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Linear constraint

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A linear constraint restricts decision variables through a linear equality or inequality.

A linear constraint restricts decision variables with a linear equality or inequality. Together with a linear objective function, linear constraints define a linear programming problem. section 2.1.4

Common constraint forms include:

  • Minimum or maximum limits, such as protein of at least 22% or fiber of at most 5%. section 2.1.4
  • Range constraints, such as calcium between 0.8% and 1.2%. section 2.1.4
  • Equality constraints, such as requiring ingredient proportions to sum to one. section 2.1.4
  • Non-negativity restrictions, which prevent negative decision-variable values. section 2.1.4

Animal feed mix

Choose proportions of corn, limestone, and soybean meal to minimize cost while satisfying calcium, protein, fiber, conservation, and non-negativity constraints. A PuLP model produces a mixture of 65% corn, 3% limestone, and 32% soybean meal, costing $0.4916 per kilogram. section 2.1.4

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Formulates equalities, inequalities, bounds, and conservation conditions, then stops at PuLP modeling and solving.
Examples
Uses an animal feed mix with calcium, protein, fiber, conservation, and non-negativity requirements.
What it assumes
Assumes decision variables and linear objectives, while demonstrating constraint types through a concrete blending problem.
What you can do after
Apply via PuLP by defining variables, constraints, an objective, and a solver call.
How it connects
Connects linear constraints with linear programming, mixed integer linear programming, objective functions, and decision variables.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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Related concepts

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