Illegal operation: pow_p( {convex}, {0.00015758} )

Nonconvex
1

clear; clc;
N = 5; M = 3; omega_delta = 0.1;H1=11e3;H2=20e3;H3=32e3;
alpha1 = pi/6; alpha2 = pi/4;omga=1;delta=2;
MN = MN; tan_diff = tan(alpha1) - tan(alpha2);
pb1=2.263206000000000e+04;
pb2=5.4749e3;
Tb=216;
Lb=1;
gmrt_con=1.5758e-4;
%
z_n_prev = ones(MN,1); %
max_iter = 50;
tan_diff=tan(alpha1) - tan(alpha2);
M_max=2max(H1,H2);
for iter = 1:max_iter
r_n_prev = 0.5 * z_n_prev * tan_diff;
cvx_begin quiet
variables z_n(MN) P_Rad(MN) P_Com(MN) p(MN) q(MN) r(MN) t(MN)
expressions r_n(MN) x_n(MN) y_n(MN) lb_expr(MN) %
expressions tilde_r_linear ph(NM) Tp(NM)
variable yy(NM) binary
tilde_r_linear = 0;
for k = 0:M-1
idx = kN + 1;
if idx <= MN
tilde_r_linear = tilde_r_linear + r_n_prev(idx)…
(0.5z_n(idx)tan_diff - r_n_prev(idx));
end
end
S_approx = 0.5omga * delta*(sum_square(r_n_prev) + 2*tilde_r_linear)*N;
maximize(S_approx)

subject to

z_n <= H2 + M_max*(1 - yy);
z_n >= H2 - M_max*yy;

for nn=1:MN
lb_expr(nn)=inv_pos(Tb + Lb(z_n(nn)-H2));
% exp_term = exp(gmrt_con * log(Tb * lb_expr)); % Logarithmic transformation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
ph(nn) = yy(nn) * pb1 * (-gmrt_conexp(z_n(nn)-H1)) + …
(1 - yy(nn)) * pb2 pow_p(Tblb_expr(nn), gmrt_con);%(Tblb_expr(nn))^gmrt_con;%(Tblb_expr(nn)).^gmrt_con;%%(Tblb_expr.^gmrt_con);%exp_term;%
Tp(nn) = yy(nn) * Tb + (1 - yy(nn)) * (Tb + Lb(z_n(nn)-H2));
end
cvx_end
end
how to solve this error?
Illegal operation: pow_p( {convex}, {0.00015758} )

2

You have violated the rules:

help pow_p

 pow_p   Positive branch of the power function.
    pow_p(X,P) computes a convex or concave branch of the power function:
            P < 0: pow_p(X,P) = X.^P if X >  0, +Inf otherwise
       0 <= P < 1: pow_p(X,P) = X.^P if X >= 0, -Inf otherwise
       1 <= P    : pow_p(X,P) = X.^P if X >= 0, +Inf otherwise
    Both P and X must be real.
 
    Disciplined convex programming information:
        The geometry of pow_p(X,P) depends on the precise value of P,
        which must be a real constant:
                 P < 0: convex  and nonincreasing; X must be concave.
            0 <= P < 1: concave and nondecreasing; X must be concave.
            1 <= P    : convex  and nonmonotonic;  X must be affine.
        In all cases, X must be real.

However, your code, as shown, does not do anything with ph, whose computation involves the illegal operation. Did you omit the code which uses it because you got the error? If so, have you proven the optimization problem is convex?

3

Hello Mark, thanks for your reply. I have omitted some code parts in the provided version because I want to check why CVX rejected my code. I know when 0<=p<=1, x should be concave. so when x is convex, what should I do to let cvx accept my code.

4

I means that CVX reports an error in this code line.

5

Please read the link.