Objective function of Log(variable) is not equal cvx_optval after cvx_end

1

Hello,

my code is that

cvx_begin
expressions sum_rate(num_user, 1)

    expressions objective_1(num_user, 1)
    expressions objective_1_tmp(num_user, 1)
    expressions tmp(num_user, 1)
    expressions tmp_tmp(num_user, 1)

    expressions objective_2(num_user, 1)
    expressions objective_2_tmp(num_user, 1)

    variable W(num_antenna, num_antenna, num_user) complex;
    variable R(num_antenna, num_antenna) complex;

    for k = 1:num_user

        for i = 1:num_user
            objective_1_tmp(k) = objective_1_tmp(k) + real(trace(channel(:,k) * channel_her(k,:) * W(:,:,i)));

            if i == k
                continue;
            end

            alpha_tmp(k) = alpha_tmp(k) + real(trace(channel(:,k) * channel_her(k,:) * W_t(:,:,i)));
        end

        alpha(k) = alpha_tmp(k) + real(trace(channel(:,k) * channel_her(k,:) * R_t)) + noise_power;
        alpha(k) = log(alpha(k)) / log(2);

        B(:,:,k) = channel(:,k) * channel_her(k,:);
        B(:,:,k) = B(:,:,k) / (alpha_tmp(k) + real(trace(channel(:,k) * channel_her(k,:) * R_t)) + noise_power);
        B(:,:,k) = B(:,:,k) / log(2);

        for i = 1:num_user

            if i == k
                continue;
            end

            objective_2_tmp(k) = objective_2_tmp(k) + real(trace(B(:,:,k) * (W(:,:,i) - W_t(:,:,i))));
        end

        tmp(k) = objective_1_tmp(k) + real(trace(channel(:,k) * channel_her(k,:) * R)) + noise_power;
        tmp_tmp(k) = log(tmp(k));
        objective_1(k) = tmp_tmp(k) / log(2);

        objective_2(k) = alpha(k) + objective_2_tmp(k) + real(trace(B(:,:,k) * (R - R_t)));

        sum_rate(k) = objective_1(k) - objective_2(k);

        sensing_constraint_tmp = sensing_constraint_tmp + W(:,:,k);
        power_constraint_tmp = power_constraint_tmp + real(trace(W(:,:,k)));
    end

    maximize(sum(sum_rate));

    subject to

        for k = 1:num_user
            W(:,:,k) == hermitian_semidefinite(num_antenna);
        end

        R == hermitian_semidefinite(num_antenna);
        
        power_constraint = power_constraint_tmp + real(trace(R));
        power_constraint <= p_max;

        for j = 1:num_target

            distance_target = get_distance(uav, target(j,:));
            sterring_target = get_steering(distance_target);
            sterring_target_her = transpose(conj(sterring_target));

            sensing_constraint = real(sterring_target_her * (sensing_constraint_tmp + R) * sterring_target);
            sensing_constraint >= sensing_th * distance_target^2;

        end
cvx_end

among them,

tmp(k) = objective_1_tmp(k) + real(trace(channel(:,k) * channel_her(k,:slight_smile: * R)) + noise_power;
tmp_tmp(k) = log(tmp(k));

tmp(k) is cvx real affine expression (scalar)

tmp_tmp(k) is cvx concave expression (scalar)

but after cvx_end

tmp(1) is 3.6746e-11, tmp_tmp(1) is -18.4045 but log(tmp(1)) is -24.0270

It is not same for all k
2

This is addressed in I wonder why the cvx_optval value is different from the object value obtained through W and R obtained through CVX even though cvx_status is solved - #4 by Mark_L_Stone .

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