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# Documentation

## Lagrange Multiplier Structures

Constrained optimization involves a set of Lagrange multipliers, as described in First-Order Optimality Measure. Solvers return estimated Lagrange multipliers in a structure. The structure is called lambda, since the conventional symbol for Lagrange multipliers is the Greek letter lambda (λ). The structure separates the multipliers into the following types, called fields:

• lower, associated with lower bounds

• upper, associated with upper bounds

• eqlin, associated with linear equalities

• ineqlin, associated with linear inequalities

• eqnonlin, associated with nonlinear equalities

• ineqnonlin, associated with nonlinear inequalities

To access, for example, the nonlinear inequality field of a Lagrange multiplier structure, enter lambda.inqnonlin. To access the third element of the Lagrange multiplier associated with lower bounds, enter lambda.lower(3).

The content of the Lagrange multiplier structure depends on the solver. For example, linear programming has no nonlinearities, so it does not have eqnonlin or ineqnonlin fields. Each applicable solver's function reference pages contains a description of its Lagrange multiplier structure under the heading "Outputs."