active and inactive constraints


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PDF OPTIMIZATION WITH CONSTRAINTS

As in Chapter 3 B is the set of equality and active inequality constraints and J is the set of inactive inequality constraints The first term measures the 

  • optimization problems.
    Unconstrained simply means that the choice variable can take on any value—there are no restrictions.
    Constrained means that the choice variable can only take on certain values within a larger range.

  • What is an active inequality constraint?

    Active constraint: An inequality constraint gi(x) ≤ 0 is said to be active (or tight) at a design point x(k) if it is satisfied as an equality at that point (ie, gi(x(k)) = 0).

  • What are the two types of constraints in constrained optimization?

    Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.

  • How can we tell if a constraint is active?

    This is explained in the Related Solution listed below.
    One way to determine which constraints are active is to check the Lagrange multipliers specified in the LAMBDA output parameter of FMINCON.
    Any nonzero component of LAMBDA indicates an active constraint (not strictly, see below).

  • If any of the constraint lines do not pass through the optimal point, those constraints are called inactive. In general, we ignore the constraints at 0 and focus on the constraints generated by limits on resources. An active constraint means that this factor is causing the limitation on the objective function.
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