** Next:** Gradient Projection Algorithm
** Up:** Optimization
** Previous:** Optimization

The goal of the proposed algorithm is to find a vector of model
parameters such that we minimize Kelley (1999)
| |
(1) |

where
| |
(2) |

with *l*_{i} and *u*_{i} being the lower and upper bounds for the model
*x*_{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 *i*th constraint are active/inactive are
called the active/inactive sets *A*(*x*)/*I*(*x*). Most of the algorithms
used to solve bound constrained problems first identify *A*(*x*) and then
solve the minimization problem for the free variables of *I*(*x*).

** Next:** Gradient Projection Algorithm
** Up:** Optimization
** Previous:** Optimization
Stanford Exploration Project

10/23/2004