The Steepest Descent Algorithm for Unconstrained Optimization and ...
The Steepest Descent Algorithm for Unconstrained Optimization and ...
The Steepest Descent Algorithm for Unconstrained Optimization and ...
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Here the domain of f(x) is X = {x ∈R | b − Ax > 0}. Given<br />
¯x ∈ X <strong>and</strong> a direction d¯, the line-search problem is:<br />
n<br />
a<br />
point<br />
∑<br />
LS : minimize h(α) := f(¯ x + αd¯) = − m ln(b i − A i (¯ x + αd¯))<br />
i=1<br />
s.t. b − A(¯x + αd¯) > 0.<br />
St<strong>and</strong>ard arithmetic manipulation can be used to establish that<br />
b − A(¯ x + αd¯) > 0 if <strong>and</strong> only if α