Inversion algorithms are very important in quantitative remote sensing. Currently

the classic least square method is still used widely. We suggest that remote sensing inversions are often typical constrained optimization problems. Many good constrained optimization methods may be used in remote sensing. After a brief review of the constrained optimization methods

we discuss the widely used augmented Lagrange multiplier method in detail. Only one penalty factor is used in this method

even if this factor is not required to be infinitive in theory

it may still increase larger and larger to meet several constraints with very different magnitudes. As a result

similar to the penalty function method

the ill-posed problem and low efficiency still bother the augmented Lagrange multiplier method. As a solution

we extend the penalty factor to be a diagonal penalty matrix

and present an extended augmented Lagrange multiplier method. Because different constraints are given different penalty factors in this new method

a priori knowledge can be used to help decrease the ill-posed problem and increase the iteration speed. After proving this new method in theory

we do detailed simulation and inversion as further validation. It is clear from the statistical analysis that the rate-of-convergence of our method has been improved of about 30 percent compared with the original penalty factor based method but with similar accuracies. Furthermore

it is also found that our extended method is resistant to ill-posed problems.