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In this section, I present the problem of finding simple bounds
and the method that solves it.
The goal of bound-constrained optimization is to find a vector of model
parameters such that we minimize
| |
(1) |
where
| |
(2) |
with l_{i} and u_{i} being the lower and upper bounds for the model
m_{i}, respectively. In this case, l_{i} and u_{i} are called simple
bounds. They can be different for each point of the model space. The
model vector that obeys equation (1) is called .
The sets of indices i for which the ith constraint are active/inactive are
called the active/inactive sets A(m)/I(m). Most of the algorithms
used to solve bound constrained problems first identify A(m) and then
solve the minimization problem for the free variables of I(m).