Nonlinear Optimization Examples |
The nonlinear programming (NLP) problem with one objective function
and
constraint functions
, which are continuously differentiable, is defined as follows:
In the preceding notation,
is the dimension of the function
, and
is the number of equality constraints. The linear combination of objective and constraint functions
is the Lagrange function, and the coefficients
are the Lagrange multipliers.
If the functions
and
are twice differentiable, the point
is an isolated local minimizer of the NLP problem, if there exists a vector
that meets the following conditions:
Kuhn-Tucker conditions
second-order condition
Each nonzero vector
with
satisfies
In practice, you cannot expect the constraint functions
to vanish within machine precision, and determining the set of active constraints at the solution
might not be simple.
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