I want to solve the program;

||Ax-b||2

lb<=x<= ub

When the lb=0 and ub=1, the solutions of the program through cvx is correct.

the output of the cvx as follows:

## number of iterations = 32

primal objective value = -1.23450801e-01

dual objective value = -1.23450811e-01

gap := trace(XZ) = 1.03e-08

relative gap = 8.28e-09

actual relative gap = 8.08e-09

rel. primal infeas = 1.82e-11

rel. dual infeas = 2.60e-12

norm(X), norm(y), norm(Z) = 5.3e+00, 8.0e-01, 3.4e+01

norm(A), norm(b), norm© = 7.7e+01, 2.0e+00, 3.5e+01

Total CPU time (secs) = 2.07

CPU time per iteration = 0.06

termination code = 0

DIMACS: 1.8e-11 0.0e+00 4.5e-11 0.0e+00 8.1e-09 8.3e-09

## Status: Solved

Optimal value (cvx_optval): +0.123451

** However, if the lb=0 and ub=1, the solutions of the program through cvx is incorrect. **

**the last status of cvx is Inaccurate/Solved**

the output of the cvx as follows:

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.197869e-17.

number of iterations = 19

primal objective value = -1.64523804e-02

dual objective value = -1.64549538e-02

gap := trace(XZ) = 2.56e-06

relative gap = 2.48e-06

actual relative gap = 2.49e-06

rel. primal infeas = 1.02e-07

rel. dual infeas = 2.39e-11

norm(X), norm(y), norm(Z) = 1.0e+00, 1.4e+00, 4.8e+01

norm(A), norm(b), norm© = 7.7e+01, 2.0e+00, 4.9e+01

Total CPU time (secs) = 1.19

CPU time per iteration = 0.06

termination code = -7

DIMACS: 1.0e-07 0.0e+00 3.9e-10 0.0e+00 2.5e-06 2.5e-06

Status: Inaccurate/Solved

Optimal value (cvx_optval): +0.016455

if you know the reason, please tell me!

Thank you very much.