Types of Constraints

Optimization · Axiom Academy

Discover how different constraints shape the world of feasible solutions. In optimization, constraints define the rules that solutions must follow. Click on each constraint type to see what makes it unique. Equality Constraints: Lines and Surfaces Explore how an equality constraint h(x) = 0 restricts solutions to a line. Adjust the slider to change the constraint parameter. Inequality Constraints: Half-Spaces Now see how an inequality constraint g(x) ≤ 0 creates an entire region of feasible points. Move the sliders to explore both sides of the boundary. Bound Constraints: A Special Case Adjust the bounds on x and y to see how they create a rectangular feasible region. Bounds are special inequalities that limit individual variables. Geometry: Define curves (2D) or surfaces (higher dimensions) that solutions must lie exactly on Effect: Reduce the problem's dimensionality Examples: Conservation laws, balance equations Geometry: Define half-spaces or regions where solutions are allowed Effect: Can be active (binding) or inactive at the optimal solution Examples: Resource limits, capacity constraints Geometry: Create box-shaped feasible regions Effect: Special case of inequality constraints, handled efficiently Examples: Non-negativity, physical limits

This is the written version of the interactive lesson above. See the full Optimization course.