Imposing constraint on gradient coefficients in NonLinear optimization

I'm trying to solve a non linear 6 dimensional optimization problem, using a gradient which I calculate (6 dimensional).

I would like to influence the gradient coefficients in such a way that Coeff(1) == Coeff(2) == Coeff(3) and Coeff(4)==Coeff(5)==Coeff(6)

Is this possible?

Thanks! Jonathan

Answer 1

[Alan Weiss]

I suppose that you could try to minimize the sum of the squares of the differences between various coefficients:

 (Coeff(1) - Coeff(2))^2 + (Coeff(1) - Coeff(3))^2 + (Coeff(4) - Coeff(5))^2 + (Coeff(4) - Coeff(6))^2

You might want to use lsqnonlin and have your vector be (coeff(1) - coeff(2), coeff(1) - coeff(3), ...)

Alan Weiss

MATLAB mathematical toolbox documentation

[Jonathan]

Thanks for the answer, but that wasn't quite what I was asking. I will try rephrasing.

I am trying to solve an optimization problem, minimizing a scalar energy functional, which is a function of 6 parameters - 3 translation parameters and 3 rotation parameters.

I'm trying to feed the 6 dimensional calculated gradient into a gradient based optimization algorithm.

The constrain I want to impose is that in each iteration, all translation gradients have the same step size, and all rotation gradients have a second step size.

If t is the translation vector, r the rotation vector, at iteration i the propagation will be:

[t(1, i), t(2, i), t(3, i), r(1, i), r(2, i), r(3, i)] = [t(1, i-1), t(2, i-1), t(3, i-1), r(1, i-1), r(2, i-1), r(3, i-1)] - [a, a, a, b, b, b].*[grad(1), grad(2), grad(3), grad(4), grad(5), grad(6)]

Is this possible? Thanks Jonathan

[Sean de Wolski]

Why do you want that additional constraint? You might be able to get it by bounding with DiffMinChange and DiffMaxChange in the options:

http://www.mathworks.com/help/releases/R2014a/optim/ug/fmincon.html#f854721