Cvx_optval changes over iteration

1

Dear everyone,
Why the optimal value is rapidly increasing after only 2 iterations ?

loop | N | M | iteration
1 | 3 | 10 | 1

Calling SDPT3 4.0: 38 variables, 17 equality constraints

num. of constraints = 17
dim. of socp var = 38, num. of socp blk = 10

SDPT3: Infeasible path-following algorithms

version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

0|0.000|0.000|2.4e+00|6.5e+00|3.2e+03| 3.404522e+01 0.000000e+00| 0:0:00| chol 1 1
1|0.884|0.892|2.7e-01|8.0e-01|4.3e+02| 3.246926e+01 -4.634346e+01| 0:0:00| chol 1 1
2|0.759|0.762|6.6e-02|2.0e-01|1.2e+02| 1.798211e+01 -2.256013e+01| 0:0:00| chol 1 1
3|0.809|0.752|1.3e-02|5.0e-02|3.8e+01| 8.137048e+00 -1.278402e+01| 0:0:00| chol 1 1
4|0.965|0.957|4.4e-04|4.7e-03|5.7e+00| 1.464427e+00 -3.321173e+00| 0:0:00| chol 1 1
5|0.935|0.802|2.9e-05|1.0e-03|1.3e+00|-1.098037e-01 -1.226895e+00| 0:0:00| chol 1 1
6|0.802|0.856|5.7e-06|1.6e-04|3.3e-01|-3.968527e-01 -6.924265e-01| 0:0:00| chol 1 1
7|0.845|0.796|8.8e-07|3.3e-05|9.2e-02|-4.929915e-01 -5.774736e-01| 0:0:00| chol 1 1
8|0.827|0.879|1.5e-07|4.2e-06|2.2e-02|-5.179931e-01 -5.391711e-01| 0:0:00| chol 1 1
9|0.892|0.844|1.6e-08|6.8e-07|5.0e-03|-5.250811e-01 -5.299553e-01| 0:0:00| chol 1 1
10|0.842|0.892|2.6e-09|7.7e-08|1.1e-03|-5.265259e-01 -5.276078e-01| 0:0:00| chol 1 1
11|0.881|0.822|3.1e-10|1.4e-08|2.7e-04|-5.268880e-01 -5.271525e-01| 0:0:00| chol 1 1
12|0.812|0.887|5.7e-11|1.7e-09|6.4e-05|-5.269608e-01 -5.270244e-01| 0:0:00| chol 1 1
13|0.890|0.806|6.3e-12|3.4e-10|1.6e-05|-5.269824e-01 -5.269983e-01| 0:0:00| chol 1 1
14|0.814|0.532|1.2e-12|1.6e-10|7.1e-06|-5.269867e-01 -5.269937e-01| 0:0:00| chol 1 1
15|1.000|0.528|2.4e-14|7.6e-11|3.3e-06|-5.269877e-01 -5.269911e-01| 0:0:00| chol 1 1
16|1.000|0.517|9.9e-15|3.7e-11|1.7e-06|-5.269881e-01 -5.269897e-01| 0:0:00| chol 1 1
17|1.000|0.516|8.0e-15|1.9e-11|8.7e-07|-5.269882e-01 -5.269891e-01| 0:0:00| chol 1 1
18|1.000|0.514|3.0e-15|1.0e-11|4.5e-07|-5.269883e-01 -5.269887e-01| 0:0:00| chol 1 1
19|1.000|0.513|7.1e-15|6.0e-12|2.4e-07|-5.269883e-01 -5.269885e-01| 0:0:00| chol 1 1
20|1.000|0.513|6.2e-15|3.9e-12|1.3e-07|-5.269883e-01 -5.269884e-01| 0:0:00| chol 1 1
21|1.000|0.512|3.4e-15|2.9e-12|6.6e-08|-5.269883e-01 -5.269884e-01| 0:0:00| chol 1 1
22|1.000|0.512|7.0e-15|2.4e-12|3.5e-08|-5.269883e-01 -5.269883e-01| 0:0:00| chol 1 1
23|1.000|0.511|2.2e-15|2.2e-12|1.9e-08|-5.269883e-01 -5.269883e-01| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08

number of iterations = 23
primal objective value = -5.26988306e-01
dual objective value = -5.26988324e-01
gap := trace(XZ) = 1.90e-08
relative gap = 9.24e-09
actual relative gap = 8.98e-09
rel. primal infeas (scaled problem) = 2.18e-15
rel. dual " " " = 2.18e-12
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 3.8e+02, 8.6e-01, 9.5e-01
norm(A), norm(b), norm© = 7.5e+00, 1.0e+02, 1.4e+00
Total CPU time (secs) = 0.26
CPU time per iteration = 0.01
termination code = 0
DIMACS: 2.2e-15 0.0e+00 2.5e-12 0.0e+00 9.0e-09 9.2e-09

Status: Solved
Optimal value (cvx_optval): +0.526988

Calling SDPT3 4.0: 64 variables, 16 equality constraints

num. of constraints = 16
dim. of socp var = 24, num. of socp blk = 8
dim. of free var = 40
*** convert ublk to linear blk

SDPT3: homogeneous self-dual path-following algorithms

version predcorr gam expon
NT 1 0.000 1
it pstep dstep pinfeas dinfeas gap mean(obj) cputime kap tau theta

0|0.000|0.000|1.4e+00|1.1e+01|2.0e+02| 1.765643e-01| 0:0:00|2.0e+02|1.0e+00|1.0e+00| chol 1 1
1|0.884|0.884|3.4e-01|2.7e+00|5.8e+01|-1.868935e-01| 0:0:00|4.2e+01|9.3e-01|2.2e-01| chol 1 1
2|1.000|1.000|4.8e-02|3.9e-01|1.0e+01|-1.086857e-01| 0:0:00|4.0e+00|8.6e-01|2.9e-02| chol 1 1
3|0.896|0.896|5.9e-03|5.4e-02|1.3e+00| 1.075089e-02| 0:0:00|2.3e-01|9.2e-01|3.8e-03| chol 1 1
4|1.000|1.000|2.3e-03|2.5e-02|6.6e-01|-1.465218e-02| 0:0:00|2.9e-02|8.6e-01|1.4e-03| chol 1 1
5|0.840|0.840|7.2e-04|1.2e-02|1.7e-01|-2.207309e-02| 0:0:00|1.3e-03|1.1e+00|5.6e-04| chol 1 1
6|0.703|0.703|4.4e-04|9.5e-03|1.1e-01|-3.494133e-02| 0:0:00|1.6e-03|1.1e+00|3.4e-04| chol 1 1
7|1.000|1.000|1.7e-04|6.7e-03|4.2e-02|-4.268790e-02| 0:0:00|1.0e-03|1.2e+00|1.4e-04| chol 1 1
8|0.924|0.924|8.2e-05|5.5e-03|2.0e-02|-5.186870e-02| 0:0:00|5.4e-04|1.2e+00|6.8e-05| chol 1 1
9|0.674|0.674|5.3e-05|4.9e-03|1.3e-02|-5.660817e-02| 0:0:00|3.4e-04|1.1e+00|4.2e-05| chol 1 1
10|0.109|0.109|5.0e-05|4.9e-03|1.6e-02|-6.464351e-02| 0:0:00|3.5e-04|1.0e+00|3.6e-05| chol 1 1
11|0.101|0.101|4.5e-05|4.9e-03|2.3e-02|-7.615881e-02| 0:0:00|3.8e-04|9.1e-01|2.9e-05| chol 1 1
12|0.202|0.202|6.5e-05|4.7e-03|2.4e-02|-7.351994e-02| 0:0:00|3.2e-04|9.6e-01|4.4e-05| chol 1 1
13|0.229|0.229|2.8e-05|4.9e-03|7.2e-02|-1.269476e-01| 0:0:00|4.3e-04|5.6e-01|1.1e-05| chol 1 1
14|0.874|0.874|1.7e-04|4.1e-03|7.4e-02|-1.137064e-01| 0:0:00|3.0e-04|6.9e-01|8.3e-05| chol 1 1
15|0.829|0.829|1.1e-04|3.3e-03|9.2e-02|-2.006705e-01| 0:0:00|5.9e-04|3.8e-01|3.0e-05| chol 1 1
16|0.835|0.835|1.1e-04|3.0e-03|1.3e-01|-2.659905e-01| 0:0:00|5.7e-04|2.6e-01|1.9e-05| chol 1 1
17|1.000|1.000|4.7e-05|2.2e-03|5.2e-02|-2.826040e-01| 0:0:00|2.8e-04|2.8e-01|9.1e-06| chol 1 1
18|1.000|1.000|1.8e-05|1.8e-03|2.1e-02|-3.127842e-01| 0:0:00|1.5e-04|2.6e-01|3.3e-06| chol 1 1
19|1.000|1.000|8.9e-06|1.6e-03|1.1e-02|-3.348155e-01| 0:0:01|6.4e-05|2.5e-01|1.6e-06| chol 1 1
20|1.000|1.000|1.1e-05|8.4e-04|1.7e-02|-3.982401e-01| 0:0:01|3.8e-05|2.1e-01|1.6e-06| chol 1 1
21|0.772|0.772|6.8e-06|3.3e-04|2.2e-02|-4.524484e-01| 0:0:01|4.2e-05|1.6e-01|7.8e-07| chol 1 1
22|0.961|0.961|8.9e-07|7.6e-05|1.9e-03|-4.695506e-01| 0:0:01|3.5e-05|1.7e-01|1.0e-07| chol 1 1
23|0.996|0.996|3.5e-07|3.3e-05|6.4e-04|-4.731781e-01| 0:0:01|3.6e-06|1.6e-01|4.0e-08| chol 1 1
24|1.000|1.000|8.2e-08|1.6e-05|1.5e-04|-4.747139e-01| 0:0:01|9.7e-07|1.7e-01|9.6e-09| chol 1 1
25|0.923|0.923|3.0e-08|8.4e-06|5.2e-05|-4.753828e-01| 0:0:01|2.9e-07|1.7e-01|3.5e-09| chol 1 1
26|0.909|0.909|1.1e-08|4.3e-06|2.0e-05|-4.757549e-01| 0:0:01|1.0e-07|1.7e-01|1.4e-09| chol 1 1
27|0.926|0.926|5.1e-09|2.1e-06|7.0e-06|-4.759521e-01| 0:0:01|3.9e-08|1.7e-01|4.7e-10| chol 1 1
28|0.942|0.942|1.5e-08|1.0e-06|2.3e-06|-4.760492e-01| 0:0:01|1.3e-08|1.7e-01|1.6e-10| chol 1 1
29|0.960|0.960|3.9e-08|5.0e-07|6.9e-07|-4.760966e-01| 0:0:01|4.2e-09|1.7e-01|4.7e-11| chol 1 1
30|0.874|0.874|2.4e-08|7.6e-08|1.7e-07|-4.761349e-01| 0:0:01|1.6e-09|1.7e-01|1.0e-11| chol 1 1
31|0.973|0.973|3.8e-08|2.5e-09|1.1e-08|-4.761415e-01| 0:0:01|3.2e-10|1.7e-01|1.6e-12| chol 1 1
stop: primal infeas has deteriorated too much, 1.6e-06 1, 0, 1
32|0.723|0.723|3.8e-08|2.5e-09|1.1e-08|-4.761415e-01| 0:0:01|3.2e-10|1.7e-01|1.6e-12|

number of iterations = 32
primal objective value = -4.76141742e-01
dual objective value = -4.76141298e-01
gap := trace(XZ) = 1.09e-08
relative gap = 7.36e-09
actual relative gap = -2.28e-07
rel. primal infeas = 3.85e-08
rel. dual infeas = 2.52e-09
norm(X), norm(y), norm(Z) = 7.1e+02, 8.6e-01, 9.5e-01
norm(A), norm(b), norm© = 1.5e+01, 1.1e+00, 4.0e-01
Total CPU time (secs) = 0.63
CPU time per iteration = 0.02
termination code = -7
DIMACS: 3.8e-08 0.0e+00 2.5e-09 0.0e+00 -2.3e-07 5.6e-09

Status: Inaccurate/Solved
Optimal value (cvx_optval): +0.526988

rate1 =

     0    3.7511

rate2 =

     0    4.1794

rate3 =

     0    2.2208

1 | 3 | 10 | 2

Calling SDPT3 4.0: 38 variables, 17 equality constraints

num. of constraints = 17
dim. of socp var = 38, num. of socp blk = 10

SDPT3: Infeasible path-following algorithms

version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

0|0.000|0.000|2.5e+00|3.3e+00|2.5e+04| 5.069004e+01 0.000000e+00| 0:0:00| chol 1 1
1|0.856|0.862|3.6e-01|4.7e-01|3.7e+03|-3.020900e+02 -5.622369e+02| 0:0:00| chol 1 1
2|0.547|0.550|1.6e-01|2.1e-01|1.8e+03|-3.214939e+02 -3.608389e+02| 0:0:00| chol 1 1
3|0.548|0.535|7.4e-02|9.8e-02|9.7e+02|-2.845743e+02 -2.620658e+02| 0:0:00| chol 1 1
4|0.667|0.597|2.5e-02|4.6e-02|4.9e+02|-1.985126e+02 -2.097468e+02| 0:0:00| chol 1 1
5|1.000|0.764|3.5e-08|1.3e-02|1.5e+02|-9.351235e+01 -1.745835e+02| 0:0:00| chol 1 1
6|0.804|0.929|1.9e-08|9.6e-04|2.1e+01|-1.257974e+02 -1.406977e+02| 0:0:00| chol 1 1
7|0.832|0.923|7.8e-09|7.4e-05|3.7e+00|-1.321355e+02 -1.354178e+02| 0:0:00| chol 1 1
8|0.857|0.844|4.4e-09|1.2e-05|9.2e-01|-1.334735e+02 -1.343365e+02| 0:0:00| chol 1 1
9|0.819|0.900|1.3e-09|1.2e-06|2.1e-01|-1.337530e+02 -1.339575e+02| 0:0:00| chol 1 1
10|0.896|0.810|1.4e-10|2.4e-07|5.1e-02|-1.338301e+02 -1.338796e+02| 0:0:00| chol 1 1
11|0.814|0.897|2.6e-11|2.7e-08|1.2e-02|-1.338446e+02 -1.338562e+02| 0:0:00| chol 1 1
12|0.892|0.805|2.8e-12|5.3e-09|2.9e-03|-1.338487e+02 -1.338516e+02| 0:0:00| chol 1 1
13|0.803|0.905|5.5e-13|5.1e-10|6.8e-04|-1.338495e+02 -1.338501e+02| 0:0:00| chol 1 1
14|0.904|0.792|5.9e-14|1.1e-10|1.7e-04|-1.338497e+02 -1.338499e+02| 0:0:00| chol 1 1
15|0.792|0.920|3.2e-14|9.5e-12|3.8e-05|-1.338497e+02 -1.338498e+02| 0:0:00| chol 1 1
16|0.916|0.778|6.7e-14|3.1e-12|9.6e-06|-1.338498e+02 -1.338498e+02| 0:0:00| chol 1 1
17|0.780|0.534|2.4e-15|2.4e-12|4.4e-06|-1.338498e+02 -1.338498e+02| 0:0:00| chol 1 1
18|1.000|0.529|4.5e-14|2.2e-12|2.1e-06|-1.338498e+02 -1.338498e+02| 0:0:00|
stop: max(relative gap, infeasibilities) < 1.49e-08

number of iterations = 18
primal objective value = -1.33849763e+02
dual objective value = -1.33849765e+02
gap := trace(XZ) = 2.10e-06
relative gap = 7.83e-09
actual relative gap = 7.79e-09
rel. primal infeas (scaled problem) = 4.50e-14
rel. dual " " " = 2.15e-12
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 6.8e+02, 2.6e+02, 2.6e+02
norm(A), norm(b), norm© = 8.5e+00, 1.0e+02, 2.2e+01
Total CPU time (secs) = 0.15
CPU time per iteration = 0.01
termination code = 0
DIMACS: 4.5e-14 0.0e+00 2.4e-12 0.0e+00 7.8e-09 7.8e-09

Status: Solved
Optimal value (cvx_optval): +133.85

Calling SDPT3 4.0: 64 variables, 16 equality constraints

num. of constraints = 16
dim. of socp var = 24, num. of socp blk = 8
dim. of free var = 40
*** convert ublk to linear blk

SDPT3: homogeneous self-dual path-following algorithms

version predcorr gam expon
NT 1 0.000 1
it pstep dstep pinfeas dinfeas gap mean(obj) cputime kap tau theta

0|0.000|0.000|1.2e+00|2.0e+00|2.0e+02| 4.350676e+00| 0:0:00|2.0e+02|1.0e+00|1.0e+00| chol 1 1
1|0.039|0.039|1.2e+00|2.0e+00|2.1e+02| 1.271940e+00| 0:0:00|2.0e+02|1.0e+00|9.9e-01| chol 1 1
2|0.042|0.042|1.2e+00|2.0e+00|2.1e+02|-1.521430e+00| 0:0:00|2.0e+02|1.0e+00|9.8e-01| chol 1 1
3|0.039|0.039|1.2e+00|2.0e+00|2.3e+02|-3.704424e+00| 0:0:00|1.9e+02|9.8e-01|9.6e-01| chol 1 1
4|0.043|0.043|1.2e+00|2.0e+00|2.4e+02|-5.863267e+00| 0:0:00|1.9e+02|9.5e-01|9.5e-01| chol 1 1
5|0.041|0.041|1.2e+00|2.0e+00|2.4e+02|-7.212806e+00| 0:0:00|1.9e+02|9.5e-01|9.3e-01| chol 1 1
6|0.045|0.045|1.2e+00|2.1e+00|2.6e+02|-9.945550e+00| 0:0:00|1.9e+02|9.3e-01|9.2e-01| chol 1 1
7|0.081|0.081|1.2e+00|2.1e+00|2.8e+02|-1.082445e+01| 0:0:00|1.8e+02|8.9e-01|8.8e-01| chol 1 1
8|0.138|0.138|1.2e+00|2.1e+00|2.8e+02|-1.639245e+01| 0:0:00|1.7e+02|8.9e-01|8.3e-01| chol 1 1
9|0.214|0.214|1.2e+00|2.1e+00|3.4e+02|-1.703651e+01| 0:0:00|1.5e+02|7.8e-01|7.4e-01| chol 1 1
10|0.253|0.253|1.2e+00|2.1e+00|4.2e+02|-1.884111e+01| 0:0:00|1.4e+02|6.8e-01|6.4e-01| chol 1 1
11|0.339|0.339|1.3e+00|2.1e+00|4.0e+02|-2.809111e+01| 0:0:00|1.2e+02|6.8e-01|5.6e-01| chol 1 1
12|0.484|0.484|1.1e+00|1.9e+00|5.2e+02|-1.298728e+01| 0:0:00|9.2e+01|5.1e-01|4.0e-01| chol 1 1
13|0.738|0.738|1.3e+00|2.1e+00|4.4e+02|-4.173530e+01| 0:0:00|6.8e+01|5.1e-01|3.1e-01| chol 1 1
14|0.962|0.962|7.3e-01|1.2e+00|8.4e+02| 2.727660e+01| 0:0:00|3.8e+01|2.6e-01|1.6e-01| chol 1 1
15|1.000|1.000|7.8e-01|1.3e+00|1.9e+03|-5.543564e+00| 0:0:00|2.0e+01|1.4e-01|9.4e-02| chol 1 1
16|1.000|1.000|3.4e-01|5.7e-01|8.6e+02| 9.093199e+01| 0:0:00|3.1e+00|1.4e-01|4.0e-02| chol 1 1
17|0.900|0.900|9.1e-02|1.5e-01|2.4e+02| 1.208370e+02| 0:0:00|1.5e+00|1.3e-01|1.0e-02| chol 1 1
18|0.953|0.953|4.5e-02|7.7e-02|1.0e+02| 1.213323e+02| 0:0:00|1.0e-01|1.5e-01|5.9e-03| chol 1 1
19|1.000|1.000|1.1e-02|2.0e-02|1.6e+01| 1.230475e+02| 0:0:00|8.6e-02|2.4e-01|2.3e-03| chol 1 1
20|0.923|0.923|3.3e-03|6.5e-03|3.2e+00| 1.229359e+02| 0:0:00|4.1e-03|3.5e-01|9.9e-04| chol 1 1
21|0.975|0.975|3.7e-04|2.3e-03|3.2e-01| 1.229369e+02| 0:0:00|9.7e-03|4.2e-01|1.4e-04| chol 1 1
22|0.979|0.979|1.0e-04|9.2e-04|8.9e-02| 1.229062e+02| 0:0:00|1.5e-03|4.2e-01|3.7e-05| chol 1 1
23|0.964|0.964|2.1e-05|3.6e-04|1.7e-02| 1.228919e+02| 0:0:00|4.0e-04|4.3e-01|7.6e-06| chol 1 1
24|0.973|0.973|7.4e-06|1.4e-04|6.5e-03| 1.228849e+02| 0:0:00|8.2e-05|4.3e-01|2.8e-06| chol 1 1
25|0.965|0.965|1.4e-06|5.7e-05|1.1e-03| 1.228825e+02| 0:0:00|2.9e-05|4.3e-01|5.2e-07| chol 1 1
26|0.959|0.959|4.9e-07|2.3e-05|4.3e-04| 1.228815e+02| 0:0:00|5.9e-06|4.3e-01|1.8e-07| chol 1 1
27|0.970|0.970|1.3e-07|9.1e-06|1.1e-04| 1.228811e+02| 0:0:00|1.9e-06|4.3e-01|4.9e-08| chol 1 1
28|0.959|0.959|2.8e-08|2.0e-06|2.4e-05| 1.228809e+02| 0:0:00|5.4e-07|4.3e-01|1.0e-08| chol 1 1
29|0.946|0.946|6.4e-09|4.3e-07|5.1e-06| 1.228808e+02| 0:0:00|1.3e-07|4.3e-01|2.0e-09| chol 1 1
30|0.931|0.931|7.1e-09|6.6e-08|9.4e-07| 1.228808e+02| 0:0:00|3.0e-08|4.3e-01|3.2e-09| chol 1 1
31|0.830|0.830|9.3e-08|4.8e-08|3.1e-07| 1.228808e+02| 0:0:00|8.5e-09|4.3e-01|9.9e-09| chol 1 1
32|0.557|0.557|5.3e-08|3.2e-08|1.8e-07| 1.228808e+02| 0:0:00|4.5e-09|4.3e-01|6.7e-09| chol 1 1
33|0.543|0.543|2.9e-08|1.7e-08|1.1e-07| 1.228808e+02| 0:0:00|2.5e-09|4.3e-01|3.6e-09| chol 1 1
34|0.766|0.766|1.1e-08|7.2e-09|4.1e-08| 1.228808e+02| 0:0:00|9.5e-10|4.3e-01|1.6e-09|
Stop: max(relative gap,infeasibilities) < 1.49e-08

number of iterations = 34
primal objective value = 1.22880805e+02
dual objective value = 1.22880804e+02
gap := trace(XZ) = 4.12e-08
relative gap = 3.33e-10
actual relative gap = 3.04e-09
rel. primal infeas = 1.09e-08
rel. dual infeas = 7.22e-09
norm(X), norm(y), norm(Z) = 6.7e+02, 2.6e+02, 2.6e+02
norm(A), norm(b), norm© = 9.4e+01, 2.5e+01, 6.5e+01
Total CPU time (secs) = 0.31
CPU time per iteration = 0.01
termination code = 0
DIMACS: 1.1e-08 0.0e+00 7.2e-09 0.0e+00 3.0e-09 1.7e-10

Status: Solved
Optimal value (cvx_optval): +133.85

2

Are you doing SCA? Almost anything can happen. Consider yourself lucky if it converges to anything, let alone a global, or even local optimum of the original problem.

3

Yes,I’m doing SCA. So it’s basically equivalent to rolling a die?

4

If you’re Stephen Boyd, the dice are probably loaded in your favor.

If you’re a random poster who implemented an unsafeguarded SCA, ,applied it to a new problem (not one solved in Stephen Boyd’s lecture notes), and has no experience implementing or understanding robust non-convex solvers, the dice are probably not loaded so much in your favor.

5

But I’ve tried a couple of methods to convert my problem into convex one,like fractional programming and SDP. All failed but SCA. Maybe I chose wrong model at first time.

6

Dear Mark,
Can I limit the output value of cvx_optval within magnitude 1?

7

Maybe you should use an off-the-shelf- non-convex optimizer, as available for instance, under YALMIP.