How to solve this problem? Disciplined convex programming error: Cannot perform the operation: {convex} ./ {real affine}

1

In my work, there exists the following problem:Disciplined convex programming error: Cannot perform the operation: {convex} ./ {real affine}

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In this, tao1,x1,and y1 are variables. U_tip is constant. so how to solve this problem? Hope for your solutions!

2

Presuming tao1 is nonnegative, use 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).
3

Thanks for your reply! My problem has solved using your tips. But there is a new problem as following:

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I have a try using pow_p pow_pos and pow_abs, but failed.
So how to solve this problem?
And if variable is a vector, I use “for” loop as tha above picture, then x1(i,1) only a element of vector to use. so should I ragard x1(i,1) as a vector to deal with? or a scalar?

4

I think is a variation on cube over square (How can I write this kind of constraint in cvx) and p-norm cone (https://docs.mosek.com/modeling-cookbook/powo.html#the-power-cone-s) . I’ll leave the details for someone else to work out.

5

I understand.Thank you very much!