This is my problem whose cvx_status is “failed”.

clear

clc

K = 4;

p_l = 0.0001;

k = 1e-26;

T = 1;

C = 1e3;

mode = [0 0 0 0]’;

cvx_begin

variable e_local(K) nonnegative;

```
opt_f = (1 - mode) .* ( p_l*ones(K, 1) ./ (2*k) ).^(1/3) + mode .* ( e_local ./ (k*T) - (p_l ./ k) ).^(1/3);
opt_t = (1 - mode) .* ( 2*e_local ./ (3*p_l) ) + mode .* T;
b_local = opt_f .* opt_t ./ C;
```

cvx_end

This problem does not include objective function and constraints, but it does not work with the following output:

## Calling SDPT3 4.0: 28 variables, 12 equality constraints

For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 12

dim. of sdp var = 16, num. of sdp blk = 8

dim. of linear var = 4

number of nearly dependent constraints = 8

To remove these constraints, re-run sqlp.m with OPTIONS.rmdepconstr = 1.

SDPT3: Infeasible path-following algorithms

## version predcorr gam expon scale_data

HKM 1 0.000 1 0

it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

## 0|0.000|0.000|2.0e+27|1.4e+04|8.0e+27|-4.000000e+23 0.000000e+00| 0:0:00| chol 1 2

1|0.000|0.000|2.0e+27|1.4e+04|8.1e+27|-4.000000e+23 0.000000e+00| 0:0:00| chol 1 2

2|0.981|0.981|3.8e+25|2.7e+02|1.6e+26| 5.846696e+23 0.000000e+00| 0:0:00|

sqlp stop: primal or dual is diverging, 9.2e+21

## number of iterations = 2

Total CPU time (secs) = 0.09

CPU time per iteration = 0.05

termination code = 3

DIMACS: 3.8e+25 0.0e+00 5.4e+02 0.0e+00 1.0e+00 2.7e+02

Status: Failed

Optimal value (cvx_optval): NaN

However, the following reformulated problem by inserting mode = [0 0 0 0]’ explicitly,

cvx_begin

variable e_local(K) nonnegative;

```
opt_f = ( p_l*ones(K, 1) ./ (2*k) ).^(1/3);
opt_t = ( 2*e_local ./ (3*p_l) );
b_local = opt_f .* opt_t ./ C;
```

cvx_end

works well with the following output:

Homogeneous problem detected; solution determined analytically.

Status: Solved

Optimal value (cvx_optval): +0

I want to solve the problem in the first form because I am trying to solve the problem with changing the mode.

n someone give me some help with my problem?