hi,Mark!I really need your help!
v[n] 、a[n] are Nx2,
lambda(N) refers to slack variable λ_n
beta(N) refers to slack variable β_n
1、My initial model is this:
At first, I just introducing slack variables , and let the first-order Taylor of ‖v[n]‖ equals or greater than
so the function becomes like
here is my expression of target function
2、But as for the third expression in the objective function‖a[n]‖^2/‖v[n]‖ ,even after I used quad_over_lin(pow_pos(norm(a(i,:)) ,2),lambda(i)),
It will appear “Cannot perform the operation {convex}.*{convex}” I
I think maybe my error is the same as this link Cannot perform the operation: {convex} .* {convex}, but it didn’t work .
3、so I introduced slack variables {β_n} to reformulate ‖a[n]‖^2, and let the first-order Taylor of ‖a[n]‖^2 equals or greater than β_n.
so the function becomes like
I think maybe I can add a epsilon to adjust tolerance,
it still didn’t work.What’s more, if i just run the iteration for once,i can get some wrong numbers,error will appear if there are more times of iteration.Oh no…
here I post the work space, maybe can help you understand the structure
In the future, please copy and paste code using Preformatted text icon, rather than posting an image of code.
You should have quad_iver_lin(...), not inv_pos(...)*quad_over_lin, beccause the inv_pos term is already included in quad_over_lin…
help quad_over_lin
quad_over_lin Sum of squares over linear.
Z=quad_over_lin(X,Y), where X is a vector and Y is a scalar, is equal to
SUM(ABS(X).^2)./Y if Y is positive, and +Inf otherwise. Y must be real.
If X is a matrix, quad_over_lin(X,Y) is a row vector containing the values
of quad_over_lin applied to each column. If X is an N-D array, the operation
is applied to the first non-singleton dimension of X.
quad_over_lin(X,Y,DIM) takes the sum along the dimension DIM of X.
A special value of DIM == 0 is accepted here, which is automatically
replaced with DIM == NDIMS(X) + 1. This has the effect of eliminating
the sum; thus quad_over_lin( X, Y, NDIMS(X) + 1 ) = ABS( X ).^2 ./ Y.
In all cases, Y must be compatible in the same sense as ./ with the squared
sum; that is, Y must be a scalar or the same size as SUM(ABS(X).^2,DIM).
Disciplined convex programming information:
quad_over_lin is convex, nonmontonic in X, and nonincreasing in Y.
Thus when used with CVX expressions, X must be convex (or affine)
and Y must be concave (or affine).
The invalid error is because your previous problem was infeasible, so the variable values were set to nan, which you apparently used as input to another (iteration) CVX problem, which considers nan input data in CVX expressions to be invalid.
, and let the first-order Taylor of ‖v[n]‖ equals or greater than 
