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The Interior Point NLP Solver |
Basic Definitions and Notation |
The gradient of a function is the vector of all the first partial derivatives of
and is denoted by
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where the superscript T denotes the transpose of a vector.
The Hessian matrix of , denoted by
, or simply by
, is an
symmetric matrix whose
element is the second partial derivative of
with respect to
and
. That is,
.
Consider the vector function, , whose first
elements are the equality constraint functions
, and whose last
elements are the inequality constraint functions
. That is,
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The matrix whose
th column is the gradient of the
th element of
is called the Jacobian matrix of
(or simply the Jacobian of the NLP problem) and is denoted by
. You can also use
to denote the
Jacobian matrix of the equality constraints and use
to denote the
Jacobian matrix of the inequality constraints. It is easy to see that
.
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