SLOW_PROGRESS error and an unusual bug

Dear JuMP Community,

I have previously asked a question where Huber regression gave slow progress error in MOSEK. I am now facing similar (and even bigger) issues in logistic regression and I would like to understand if I am doing any mistakes. I followed the JuMP exponential cone modeling tricks, and I did several tests. I cannot see where I am making a mistake, or if there is a bug somewhere in the code. Any support will be extremely helpful.

Problem 1: SLOW Progress
I followed exactly the logistic regression modeling tricks on the JuMP Conic optimization tutorials page. Unfortunately, I get Slow progress error. Here are the relevant functions I am using:

"Takes a model and adds a softplus constraint. See https://jump.dev/JuMP.jl/stable/tutorials/conic/logistic_regression"
function softplus(model, t_aux, linear_transform) #exponential cone constraint
# models constraints of form: log(1 + exp(linear_transform)) <= t
z = @variable(model, [1:2], lower_bound = 0.0) #anonymized variable
#add the exp-cone constraints
@constraint(model, sum(z) <= 1.0)
@constraint(model, [linear_transform - t_aux, 1, z[1]] in MOI.ExponentialCone())
@constraint(model, [-t_aux, 1, z[2]] in MOI.ExponentialCone())
end

function build_logit_model(X, y)
N, n = size(X) #N rows, n predictors
model = Model(MosekTools.Optimizer) #start the model
@variable(model, beta[1:n]) #beta coefficients
@variable(model, beta_0) #intercept
@variable(model, t[1:N]) #auxiliary variables
for i in 1:N
linear_transform = -y[i]*(X[i, :]' * beta + beta_0)
softplus(model, t[i], linear_transform)
end
# Define objective
@objective(model, Min, sum(t)) #this gives slow progress error
return model
end


Problem 2: Wrong solutions
Recall that the above exponential conic constraints were used to model constraints in the following form:
t_i \geq \log(1 + \exp( - y^i \cdot (\mathbf{\beta}^\top \mathbf{x} + \beta_0))), \ i = 1,\ldots,N
and we minimize \sum_{i=1}^N t_i.

Now, I am adding a new variable, u \geq 0, and updating the above constraints as
t_i \geq \log(1 + \exp( - y^i \cdot (\mathbf{\beta}^\top \mathbf{x} + \beta_0) + u)), \ i = 1,\ldots,N. I achieved this by replacing the previous for loop (that added softplus constraints) with:

@variable(model, u >= 0.0)
for i in 1:N
linear_transform = (-y[i]*(X[i, :]' * beta + beta_0)) + u
softplus(model, t[i], linear_transform)
end


As \log and \exp are increasing functions, at optimality we need to have u=0. However, I get results like u = 0.5.

I am attaching my MWE codes – main_test is the 10-line main file, logistic_regression_tests includes the functions. Thank you for your time.
logistic_regression_test.jl (2.5 KB)
main_test.jl (610 Bytes)

Do you have the Mosek log? It seemed to work alright when I used SCS

julia> include("/Users/Oscar/Downloads/main_test.jl")
------------------------------------------------------------------
SCS v3.2.3 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 161, constraints m: 450
cones: 	  l: linear vars: 150
e: exp vars: 300, dual exp vars: 0
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 100000, normalize: 1, rho_x: 1.00e-06
acceleration_lookback: 10, acceleration_interval: 10
lin-sys:  sparse-direct-amd-qdldl
nnz(A): 950, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
0| 1.56e+01  3.08e+00  6.28e+02 -3.09e+02  1.00e-01  9.62e-04
250| 2.32e-02  1.63e-03  6.89e-05  4.79e-02  3.26e-03  1.02e-02
475| 4.90e-04  2.06e-06  4.33e-05  1.12e-04  3.26e-03  1.78e-02
------------------------------------------------------------------
status:  solved
timings: total: 1.78e-02s = setup: 6.98e-04s + solve: 1.71e-02s
lin-sys: 3.60e-03s, cones: 1.21e-02s, accel: 4.43e-04s
------------------------------------------------------------------
objective = 0.000112
------------------------------------------------------------------
------------------------------------------------------------------
SCS v3.2.3 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 162, constraints m: 451
cones: 	  l: linear vars: 151
e: exp vars: 300, dual exp vars: 0
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 100000, normalize: 1, rho_x: 1.00e-06
acceleration_lookback: 10, acceleration_interval: 10
lin-sys:  sparse-direct-amd-qdldl
nnz(A): 1001, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
0| 1.00e+00  1.52e+00  7.46e+00  3.47e+00  1.00e-01  6.26e-04
250| 1.58e-02  2.08e-04  9.68e-04  4.45e-03  3.40e-04  1.08e-02
500| 6.67e-03  4.55e-06  2.01e-05  1.68e-04  6.72e-05  1.98e-02
525| 1.18e-03  4.92e-06  2.21e-05  1.60e-04  6.72e-05  2.07e-02
------------------------------------------------------------------
status:  solved
timings: total: 2.08e-02s = setup: 5.09e-04s + solve: 2.03e-02s
lin-sys: 4.20e-03s, cones: 1.46e-02s, accel: 2.62e-04s
------------------------------------------------------------------
objective = 0.000160
------------------------------------------------------------------
0.0011841036622605645


Thank you for your answer!

Regarding the first issue, yes SCS is slower but it does not give an error. For a case with such error, here is MOSEK’s log

Problem
Name                   :
Objective sense        : minimize
Type                   : CONIC (conic optimization problem)
Constraints            : 50
Affine conic cons.     : 100
Disjunctive cons.      : 0
Cones                  : 0
Scalar variables       : 161
Matrix variables       : 0
Integer variables      : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries                  : 1                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.00
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.00
Problem
Name                   :
Objective sense        : minimize
Type                   : CONIC (conic optimization problem)
Constraints            : 50
Affine conic cons.     : 100
Disjunctive cons.      : 0
Cones                  : 0
Scalar variables       : 161
Matrix variables       : 0
Integer variables      : 0

Optimizer  - threads                : 16
Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 100
Optimizer  - Cones                  : 101
Optimizer  - Scalar variables       : 312               conic                  : 312
Optimizer  - Semi-definite variables: 0                 scalarized             : 0
Factor     - setup time             : 0.00              dense det. time        : 0.00
Factor     - ML order time          : 0.00              GP order time          : 0.00
Factor     - nonzeros before factor : 1375              after factor           : 1375
Factor     - dense dim.             : 0                 flops                  : 7.49e+04
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.6e+00  1.3e+00  1.2e+02  0.00e+00   4.139191995e+01   -8.051020016e+01  1.0e+00  0.00
1   5.8e-01  4.7e-01  3.0e+01  5.59e-01   2.585173667e+01   -2.613361691e+01  3.7e-01  0.00
2   1.6e-01  1.3e-01  4.9e+00  7.47e-01   1.317838634e+01   -3.003032630e+00  1.0e-01  0.00
3   3.3e-02  2.7e-02  5.8e-01  7.74e-01   5.732317769e+00   1.821782393e+00   2.1e-02  0.00
4   1.1e-02  8.9e-03  1.4e-01  6.86e-01   2.665583556e+00   1.090325482e+00   6.9e-03  0.00
5   5.7e-03  4.7e-03  5.7e-02  7.14e-01   1.673192584e+00   7.418407253e-01   3.6e-03  0.01
6   2.5e-03  2.1e-03  1.8e-02  7.47e-01   9.582147151e-01   4.972977269e-01   1.6e-03  0.01
7   1.7e-03  1.4e-03  1.1e-02  7.26e-01   6.855681336e-01   3.552579988e-01   1.1e-03  0.01
8   4.2e-04  3.4e-04  1.5e-03  7.76e-01   2.533139043e-01   1.607749896e-01   2.6e-04  0.01
9   2.1e-04  1.7e-04  5.9e-04  7.71e-01   1.409415799e-01   8.946052603e-02   1.3e-04  0.01
10  4.8e-05  3.9e-05  7.4e-05  8.19e-01   4.686635109e-02   3.363332368e-02   3.0e-05  0.01
11  2.3e-05  1.9e-05  2.7e-05  8.05e-01   2.448930942e-02   1.748680533e-02   1.5e-05  0.01
12  6.5e-06  5.3e-06  4.5e-06  8.57e-01   9.083927068e-03   6.931152791e-03   4.1e-06  0.01
13  3.6e-06  3.0e-06  2.0e-06  8.14e-01   5.287226348e-03   3.997737745e-03   2.3e-06  0.01
14  7.2e-07  5.9e-07  2.0e-07  8.61e-01   1.409723787e-03   1.131556351e-03   4.6e-07  0.01
15  3.1e-07  2.5e-07  6.1e-08  8.52e-01   6.456630606e-04   5.154212171e-04   2.0e-07  0.01
16  9.4e-08  7.6e-08  1.1e-08  8.94e-01   2.308655801e-04   1.893727149e-04   5.9e-08  0.01
17  3.3e-08  2.5e-08  2.2e-09  8.84e-01   8.754891829e-05   7.284689040e-05   2.0e-08  0.01
18  2.6e-08  1.6e-08  1.2e-09  8.84e-01   5.743010263e-05   4.768850141e-05   1.2e-08  0.01
19  9.7e-09  4.0e-09  1.5e-10  9.06e-01   1.714138580e-05   1.459339583e-05   3.1e-09  0.01
20  7.6e-09  1.5e-09  3.8e-11  8.94e-01   6.889533497e-06   5.860804250e-06   1.2e-09  0.01
21  4.2e-09  4.5e-10  6.3e-12  9.39e-01   2.301303044e-06   1.987387010e-06   3.6e-10  0.01
22  3.8e-09  4.1e-10  5.4e-12  8.88e-01   2.082679362e-06   1.797260748e-06   3.2e-10  0.01
23  3.4e-09  3.8e-10  4.9e-12  8.89e-01   1.943090761e-06   1.676749874e-06   3.0e-10  0.01
24  3.6e-09  3.6e-10  4.6e-12  8.90e-01   1.872428174e-06   1.615837750e-06   2.9e-10  0.01
25  3.6e-09  3.6e-10  4.5e-12  8.90e-01   1.854984964e-06   1.600807402e-06   2.8e-10  0.02
26  3.7e-09  3.0e-10  3.5e-12  8.90e-01   1.572975573e-06   1.357818781e-06   2.4e-10  0.02
27  3.7e-09  3.0e-10  3.5e-12  8.91e-01   1.572490409e-06   1.357401071e-06   2.4e-10  0.02
28  3.4e-09  3.0e-10  3.5e-12  8.91e-01   1.564721632e-06   1.350711804e-06   2.3e-10  0.02
29  3.6e-09  3.0e-10  3.5e-12  8.92e-01   1.564480004e-06   1.350503729e-06   2.3e-10  0.02
30  3.7e-09  3.0e-10  3.5e-12  8.91e-01   1.564359171e-06   1.350399712e-06   2.3e-10  0.02
31  3.7e-09  3.0e-10  3.5e-12  8.91e-01   1.563392547e-06   1.349567382e-06   2.3e-10  0.02
32  3.4e-09  2.9e-10  3.4e-12  8.91e-01   1.547921305e-06   1.336246080e-06   2.3e-10  0.02
33  3.6e-09  2.7e-10  3.0e-12  8.91e-01   1.424382641e-06   1.229875030e-06   2.1e-10  0.02
34  1.3e-09  7.7e-11  4.9e-13  8.91e-01   4.498861209e-07   3.907514670e-07   6.1e-11  0.03
35  2.8e-09  7.4e-11  4.6e-13  1.00e+00   4.320382219e-07   3.752810550e-07   5.9e-11  0.03
36  2.3e-09  7.3e-11  4.5e-13  1.00e+00   4.253343713e-07   3.694745878e-07   5.8e-11  0.03
37  3.1e-09  7.3e-11  4.5e-13  1.00e+00   4.251732127e-07   3.693354810e-07   5.8e-11  0.03
38  3.3e-09  7.3e-11  4.5e-13  1.00e+00   4.243864314e-07   3.686537926e-07   5.8e-11  0.03
39  3.4e-09  7.3e-11  4.5e-13  9.87e-01   4.243784290e-07   3.686469288e-07   5.8e-11  0.03
40  2.9e-09  7.3e-11  4.5e-13  8.89e-01   4.242851412e-07   3.685666494e-07   5.8e-11  0.03
41  3.2e-09  7.1e-11  4.4e-13  9.60e-01   4.167771457e-07   3.620330942e-07   5.7e-11  0.03
42  2.7e-09  7.1e-11  4.3e-13  9.27e-01   4.143155083e-07   3.599063002e-07   5.6e-11  0.03
43  2.6e-09  7.0e-11  4.2e-13  1.00e+00   4.077881021e-07   3.542505467e-07   5.5e-11  0.03
44  3.1e-09  7.0e-11  4.2e-13  9.28e-01   4.074836716e-07   3.539871805e-07   5.5e-11  0.03
45  3.3e-09  7.0e-11  4.2e-13  9.15e-01   4.074726719e-07   3.539776897e-07   5.5e-11  0.03
46  3.4e-09  7.0e-11  4.2e-13  9.17e-01   4.074394898e-07   3.539489936e-07   5.5e-11  0.04
47  3.3e-09  7.0e-11  4.2e-13  9.17e-01   4.073999746e-07   3.539149326e-07   5.5e-11  0.04
48  3.3e-09  6.9e-11  4.1e-13  9.93e-01   4.019378148e-07   3.491841882e-07   5.5e-11  0.04
49  3.4e-09  6.7e-11  4.0e-13  1.00e+00   3.950313842e-07   3.431998704e-07   5.4e-11  0.04
50  3.4e-09  6.7e-11  4.0e-13  9.18e-01   3.948965063e-07   3.430833501e-07   5.4e-11  0.04
51  3.4e-09  6.7e-11  4.0e-13  9.32e-01   3.905051208e-07   3.392844759e-07   5.3e-11  0.04
52  3.2e-09  6.3e-11  3.7e-13  1.00e+00   3.720702440e-07   3.232957401e-07   5.1e-11  0.04
53  3.4e-09  6.3e-11  3.7e-13  1.00e+00   3.716938068e-07   3.229697222e-07   5.1e-11  0.04
54  3.4e-09  6.3e-11  3.7e-13  1.05e+00   3.709217824e-07   3.223064386e-07   5.0e-11  0.04
55  3.4e-09  6.3e-11  3.7e-13  1.01e+00   3.706366259e-07   3.220596767e-07   5.0e-11  0.04
56  3.4e-09  6.2e-11  3.6e-13  1.00e+00   3.652944308e-07   3.174321546e-07   5.0e-11  0.04
57  3.3e-09  6.2e-11  3.5e-13  1.00e+00   3.616423141e-07   3.142676667e-07   4.9e-11  0.04
58  3.3e-09  6.2e-11  3.5e-13  9.58e-01   3.616365254e-07   3.142626418e-07   4.9e-11  0.04
59  3.2e-09  6.0e-11  3.4e-13  1.00e+00   3.515246266e-07   3.055077031e-07   4.8e-11  0.05
60  3.3e-09  5.9e-11  3.3e-13  9.77e-01   3.448468904e-07   2.997088682e-07   4.7e-11  0.05
61  3.2e-09  5.9e-11  3.3e-13  9.57e-01   3.448262913e-07   2.996910341e-07   4.7e-11  0.05
62  3.2e-09  5.9e-11  3.3e-13  9.22e-01   3.447140061e-07   2.995938621e-07   4.7e-11  0.05
63  3.4e-09  5.9e-11  3.3e-13  1.00e+00   3.437733406e-07   2.987786562e-07   4.7e-11  0.05
64  3.5e-09  5.9e-11  3.3e-13  9.21e-01   3.437697806e-07   2.987755996e-07   4.7e-11  0.05
65  3.1e-09  5.7e-11  3.1e-13  1.00e+00   3.348668131e-07   2.910668296e-07   4.6e-11  0.05
66  3.1e-09  5.6e-11  3.1e-13  1.00e+00   3.319209257e-07   2.885170511e-07   4.5e-11  0.05
67  3.1e-09  5.6e-11  3.1e-13  9.47e-01   3.318151644e-07   2.884255094e-07   4.5e-11  0.05
68  3.1e-09  5.5e-11  3.0e-13  1.00e+00   3.235762467e-07   2.812897168e-07   4.4e-11  0.05
69  3.2e-09  5.3e-11  2.8e-13  9.99e-01   3.136621549e-07   2.727106778e-07   4.3e-11  0.05
70  3.4e-09  5.3e-11  2.8e-13  9.15e-01   3.136423355e-07   2.726935807e-07   4.3e-11  0.05
71  3.4e-09  5.3e-11  2.8e-13  1.00e+00   3.132678118e-07   2.723695400e-07   4.3e-11  0.06
72  3.3e-09  5.3e-11  2.8e-13  9.98e-01   3.115505015e-07   2.708834096e-07   4.3e-11  0.06
73  3.4e-09  5.3e-11  2.8e-13  9.90e-01   3.115349619e-07   2.708699010e-07   4.3e-11  0.06
74  3.4e-09  5.3e-11  2.8e-13  9.90e-01   3.114154829e-07   2.707662149e-07   4.3e-11  0.06
75  2.8e-09  5.2e-11  2.8e-13  1.00e+00   3.087176759e-07   2.684289369e-07   4.2e-11  0.06
76  3.4e-09  5.1e-11  2.6e-13  1.00e+00   2.989315112e-07   2.599530888e-07   4.1e-11  0.06
77  3.4e-09  5.1e-11  2.6e-13  1.00e+00   2.987921149e-07   2.598323437e-07   4.1e-11  0.06
78  3.4e-09  5.1e-11  2.6e-13  9.28e-01   2.986805021e-07   2.597357723e-07   4.1e-11  0.06
79  3.4e-09  5.1e-11  2.6e-13  1.00e+00   2.985893366e-07   2.596568331e-07   4.1e-11  0.06
80  3.3e-09  5.1e-11  2.6e-13  9.55e-01   2.985774543e-07   2.596465472e-07   4.1e-11  0.06
81  3.4e-09  5.0e-11  2.6e-13  1.00e+00   2.951291337e-07   2.566623829e-07   4.1e-11  0.06
82  2.8e-09  4.9e-11  2.5e-13  1.00e+00   2.891031983e-07   2.514401112e-07   4.0e-11  0.06
83  3.3e-09  4.9e-11  2.5e-13  9.87e-01   2.889396388e-07   2.512982402e-07   4.0e-11  0.07
84  3.4e-09  4.9e-11  2.5e-13  9.74e-01   2.889361491e-07   2.512952193e-07   4.0e-11  0.07
85  3.1e-09  4.8e-11  2.4e-13  1.00e+00   2.852736139e-07   2.481222713e-07   3.9e-11  0.07
86  3.4e-09  4.8e-11  2.4e-13  1.00e+00   2.844345767e-07   2.473945540e-07   3.9e-11  0.07
87  3.4e-09  4.8e-11  2.4e-13  1.00e+00   2.828788169e-07   2.460472347e-07   3.9e-11  0.07
88  3.5e-09  4.8e-11  2.4e-13  1.00e+00   2.827654539e-07   2.459489957e-07   3.9e-11  0.07
89  3.5e-09  4.8e-11  2.4e-13  9.25e-01   2.827650380e-07   2.459486307e-07   3.9e-11  0.07
90  3.0e-09  4.6e-11  2.3e-13  1.00e+00   2.713170489e-07   2.360269511e-07   3.7e-11  0.07
91  3.2e-09  4.5e-11  2.2e-13  1.01e+00   2.686930811e-07   2.337509781e-07   3.7e-11  0.07
92  3.2e-09  4.5e-11  2.2e-13  1.00e+00   2.653103101e-07   2.308203055e-07   3.7e-11  0.07
93  3.4e-09  4.5e-11  2.2e-13  9.47e-01   2.653055739e-07   2.308161898e-07   3.7e-11  0.07
94  3.4e-09  4.5e-11  2.2e-13  1.00e+00   2.649544201e-07   2.305116975e-07   3.7e-11  0.08
95  3.4e-09  4.4e-11  2.1e-13  1.00e+00   2.603097646e-07   2.264873363e-07   3.6e-11  0.08
96  3.4e-09  4.4e-11  2.1e-13  9.33e-01   2.602886348e-07   2.264690251e-07   3.6e-11  0.08
97  3.4e-09  4.4e-11  2.1e-13  1.00e+00   2.587306476e-07   2.251170339e-07   3.6e-11  0.08
98  3.4e-09  4.3e-11  2.1e-13  1.00e+00   2.572695532e-07   2.238494248e-07   3.5e-11  0.08
99  3.4e-09  4.3e-11  2.1e-13  1.00e+00   2.571256546e-07   2.237247876e-07   3.5e-11  0.08
100 2.5e-09  4.1e-11  1.9e-13  1.00e+00   2.450132846e-07   2.132358027e-07   3.4e-11  0.08
101 3.0e-09  4.1e-11  1.9e-13  1.00e+00   2.432477241e-07   2.117064355e-07   3.4e-11  0.08
102 2.8e-09  4.0e-11  1.9e-13  1.00e+00   2.392599609e-07   2.082537817e-07   3.3e-11  0.08
103 2.7e-09  3.9e-11  1.8e-13  1.00e+00   2.304911550e-07   2.006536907e-07   3.2e-11  0.08
104 2.8e-09  3.9e-11  1.8e-13  1.00e+00   2.303429754e-07   2.005254143e-07   3.2e-11  0.08
105 3.0e-09  3.8e-11  1.7e-13  1.00e+00   2.264872359e-07   1.971839846e-07   3.1e-11  0.08
106 3.4e-09  3.8e-11  1.7e-13  9.22e-01   2.263182867e-07   1.970377080e-07   3.1e-11  0.09
107 3.1e-09  3.8e-11  1.7e-13  9.31e-01   2.262686226e-07   1.969947856e-07   3.1e-11  0.09
108 3.4e-09  3.8e-11  1.7e-13  9.00e-01   2.262446021e-07   1.969740205e-07   3.1e-11  0.09
109 3.4e-09  3.8e-11  1.7e-13  1.00e+00   2.255803497e-07   1.963985691e-07   3.1e-11  0.09
110 2.9e-09  3.8e-11  1.7e-13  9.14e-01   2.255430817e-07   1.963663261e-07   3.1e-11  0.09
111 3.2e-09  3.7e-11  1.7e-13  1.00e+00   2.220906334e-07   1.933744651e-07   3.1e-11  0.09
112 3.4e-09  3.7e-11  1.7e-13  1.00e+00   2.209732295e-07   1.924055944e-07   3.1e-11  0.09
113 3.4e-09  3.7e-11  1.6e-13  1.00e+00   2.201478028e-07   1.916903430e-07   3.0e-11  0.09
114 2.9e-09  3.6e-11  1.6e-13  1.00e+00   2.162036786e-07   1.882704927e-07   3.0e-11  0.09
115 3.3e-09  3.6e-11  1.6e-13  9.45e-01   2.161644999e-07   1.882364856e-07   3.0e-11  0.09
116 3.2e-09  3.6e-11  1.6e-13  8.79e-01   2.161620466e-07   1.882343771e-07   3.0e-11  0.09
117 3.4e-09  3.6e-11  1.6e-13  9.88e-01   2.161339449e-07   1.882099883e-07   3.0e-11  0.10
118 3.3e-09  3.6e-11  1.5e-13  1.00e+00   2.116723332e-07   1.843404226e-07   2.9e-11  0.10
119 3.4e-09  3.6e-11  1.5e-13  9.83e-01   2.116684551e-07   1.843370703e-07   2.9e-11  0.10
120 3.3e-09  3.5e-11  1.5e-13  1.00e+00   2.086572284e-07   1.817270773e-07   2.9e-11  0.10
121 3.4e-09  3.5e-11  1.5e-13  1.00e+00   2.079947049e-07   1.811530190e-07   2.9e-11  0.10
122 3.4e-09  3.5e-11  1.5e-13  1.04e+00   2.079815621e-07   1.811416706e-07   2.9e-11  0.10
123 2.8e-09  3.4e-11  1.5e-13  1.00e+00   2.042435318e-07   1.779005127e-07   2.8e-11  0.10
124 3.2e-09  3.3e-11  1.4e-13  1.00e+00   1.995534530e-07   1.738375975e-07   2.8e-11  0.10
125 3.2e-09  3.3e-11  1.4e-13  1.00e+00   1.969163443e-07   1.715533037e-07   2.7e-11  0.10
126 3.3e-09  3.3e-11  1.4e-13  1.00e+00   1.962384737e-07   1.709656813e-07   2.7e-11  0.10
127 3.3e-09  3.3e-11  1.4e-13  1.00e+00   1.960381789e-07   1.707919713e-07   2.7e-11  0.10
128 3.4e-09  3.3e-11  1.4e-13  1.00e+00   1.954633702e-07   1.702925047e-07   2.7e-11  0.11
129 3.5e-09  3.3e-11  1.4e-13  1.00e+00   1.954624605e-07   1.702917712e-07   2.7e-11  0.11
130 3.3e-09  3.3e-11  1.4e-13  9.77e-01   1.954287570e-07   1.702624607e-07   2.7e-11  0.11
131 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.936722385e-07   1.687396017e-07   2.7e-11  0.11
132 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.934513520e-07   1.685482084e-07   2.7e-11  0.11
133 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.931180323e-07   1.682593083e-07   2.7e-11  0.11
134 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.929885403e-07   1.681469005e-07   2.7e-11  0.11
135 3.5e-09  3.2e-11  1.3e-13  1.00e+00   1.929847361e-07   1.681435653e-07   2.7e-11  0.11
136 3.5e-09  3.2e-11  1.3e-13  1.00e+00   1.929755292e-07   1.681356057e-07   2.7e-11  0.11
137 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.929683831e-07   1.681294278e-07   2.7e-11  0.11
138 3.3e-09  3.2e-11  1.3e-13  7.07e-01   1.929060433e-07   1.680756468e-07   2.7e-11  0.11
139 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.912190631e-07   1.666136520e-07   2.7e-11  0.12
140 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.912058526e-07   1.666021920e-07   2.7e-11  0.12
141 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.902509435e-07   1.657736242e-07   2.6e-11  0.12
142 3.4e-09  3.2e-11  1.3e-13  1.00e+00   1.899862823e-07   1.655442318e-07   2.6e-11  0.12
143 3.4e-09  3.2e-11  1.3e-13  9.41e-01   1.899754597e-07   1.655348730e-07   2.6e-11  0.12
144 3.1e-09  3.2e-11  1.3e-13  8.91e-01   1.899518523e-07   1.655144814e-07   2.6e-11  0.12
145 3.2e-09  3.1e-11  1.3e-13  1.00e+00   1.876498037e-07   1.635188263e-07   2.6e-11  0.12
146 3.3e-09  3.1e-11  1.3e-13  1.00e+00   1.867144670e-07   1.627082008e-07   2.6e-11  0.12
147 3.4e-09  3.1e-11  1.3e-13  1.00e+00   1.847650938e-07   1.610164915e-07   2.6e-11  0.12
148 3.4e-09  3.1e-11  1.2e-13  1.00e+00   1.841604517e-07   1.604922122e-07   2.6e-11  0.13
149 3.4e-09  3.1e-11  1.2e-13  9.88e-01   1.841503021e-07   1.604834100e-07   2.6e-11  0.13
150 3.4e-09  3.1e-11  1.2e-13  8.85e-01   1.841500863e-07   1.604832397e-07   2.6e-11  0.13
151 3.4e-09  3.1e-11  1.2e-13  1.00e+00   1.841086783e-07   1.604473218e-07   2.6e-11  0.13
152 3.5e-09  3.1e-11  1.2e-13  9.74e-01   1.840196303e-07   1.603699152e-07   2.6e-11  0.13
153 3.5e-09  3.1e-11  1.2e-13  1.00e+00   1.840140079e-07   1.603650509e-07   2.6e-11  0.13
154 3.5e-09  3.1e-11  1.2e-13  1.00e+00   1.840140079e-07   1.603650509e-07   2.6e-11  0.13
155 3.5e-09  3.1e-11  1.2e-13  1.00e+00   1.840135907e-07   1.603646798e-07   2.6e-11  0.13
156 3.3e-09  3.1e-11  1.2e-13  9.84e-01   1.839546835e-07   1.603134885e-07   2.6e-11  0.13
157 3.4e-09  3.0e-11  1.2e-13  1.00e+00   1.824430128e-07   1.590027546e-07   2.5e-11  0.14
158 3.3e-09  3.0e-11  1.2e-13  9.84e-01   1.820997856e-07   1.587051586e-07   2.5e-11  0.14
159 3.3e-09  3.0e-11  1.2e-13  1.00e+00   1.818205161e-07   1.584625203e-07   2.5e-11  0.14
160 3.4e-09  3.0e-11  1.2e-13  1.01e+00   1.817488064e-07   1.584003305e-07   2.5e-11  0.14
161 3.4e-09  3.0e-11  1.2e-13  1.00e+00   1.814670396e-07   1.581557874e-07   2.5e-11  0.14
162 3.3e-09  3.0e-11  1.2e-13  1.00e+00   1.804254155e-07   1.572554718e-07   2.5e-11  0.14
163 3.3e-09  3.0e-11  1.2e-13  1.00e+00   1.804088208e-07   1.572410408e-07   2.5e-11  0.14
164 3.3e-09  3.0e-11  1.2e-13  1.00e+00   1.803574750e-07   1.571965210e-07   2.5e-11  0.14
165 3.3e-09  3.0e-11  1.2e-13  1.00e+00   1.801890865e-07   1.570504857e-07   2.5e-11  0.14
166 3.4e-09  3.0e-11  1.2e-13  1.00e+00   1.800461355e-07   1.569264384e-07   2.5e-11  0.14
167 3.4e-09  3.0e-11  1.2e-13  1.00e+00   1.799856901e-07   1.568739266e-07   2.5e-11  0.14
168 3.4e-09  3.0e-11  1.2e-13  1.00e+00   1.799503996e-07   1.568433201e-07   2.5e-11  0.14
169 3.5e-09  3.0e-11  1.2e-13  1.00e+00   1.799499060e-07   1.568428723e-07   2.5e-11  0.15
170 3.2e-09  3.0e-11  1.2e-13  1.00e+00   1.789402933e-07   1.559656490e-07   2.5e-11  0.15
171 3.2e-09  3.0e-11  1.2e-13  9.99e-01   1.788066420e-07   1.558494562e-07   2.5e-11  0.15
172 3.4e-09  3.0e-11  1.2e-13  9.99e-01   1.768235281e-07   1.541306859e-07   2.5e-11  0.15
173 3.3e-09  2.9e-11  1.2e-13  1.00e+00   1.763202671e-07   1.536933405e-07   2.5e-11  0.15
174 3.3e-09  2.9e-11  1.2e-13  9.92e-01   1.762586076e-07   1.536397677e-07   2.5e-11  0.15
175 3.4e-09  2.9e-11  1.2e-13  1.00e+00   1.758093381e-07   1.532499990e-07   2.4e-11  0.15
176 3.4e-09  2.9e-11  1.2e-13  1.00e+00   1.757927935e-07   1.532355913e-07   2.4e-11  0.15
177 3.4e-09  2.9e-11  1.2e-13  1.00e+00   1.754123585e-07   1.529054936e-07   2.4e-11  0.15
178 3.4e-09  2.9e-11  1.1e-13  1.00e+00   1.735235587e-07   1.512648552e-07   2.4e-11  0.15
179 3.2e-09  2.9e-11  1.1e-13  1.00e+00   1.722297109e-07   1.501427954e-07   2.4e-11  0.15
180 3.4e-09  2.9e-11  1.1e-13  1.00e+00   1.721123880e-07   1.500409064e-07   2.4e-11  0.16
181 3.4e-09  2.9e-11  1.1e-13  9.91e-01   1.721112405e-07   1.500399170e-07   2.4e-11  0.16
182 3.4e-09  2.9e-11  1.1e-13  1.00e+00   1.713562460e-07   1.493849155e-07   2.4e-11  0.16
183 3.4e-09  2.9e-11  1.1e-13  1.00e+00   1.709633611e-07   1.490444029e-07   2.4e-11  0.16
184 3.5e-09  2.9e-11  1.1e-13  1.00e+00   1.709538400e-07   1.490360951e-07   2.4e-11  0.16
185 3.5e-09  2.9e-11  1.1e-13  1.00e+00   1.709538400e-07   1.490360951e-07   2.4e-11  0.16
186 3.5e-09  2.9e-11  1.1e-13  1.00e+00   1.709535296e-07   1.490358557e-07   2.4e-11  0.16
187 3.5e-09  2.9e-11  1.1e-13  1.00e+00   1.709526107e-07   1.490350141e-07   2.4e-11  0.16
188 3.4e-09  2.8e-11  1.1e-13  9.97e-01   1.708073021e-07   1.489089680e-07   2.4e-11  0.16
189 3.4e-09  2.8e-11  1.1e-13  1.00e+00   1.702991344e-07   1.484682636e-07   2.4e-11  0.16
190 3.3e-09  2.8e-11  1.1e-13  1.00e+00   1.693410114e-07   1.476377662e-07   2.4e-11  0.16
191 3.3e-09  2.8e-11  1.1e-13  1.00e+00   1.692809464e-07   1.475857419e-07   2.4e-11  0.17
192 3.3e-09  2.8e-11  1.1e-13  9.91e-01   1.691602404e-07   1.474808777e-07   2.4e-11  0.17
193 3.3e-09  2.8e-11  1.1e-13  1.00e+00   1.677554665e-07   1.462632517e-07   2.3e-11  0.17
194 3.2e-09  2.8e-11  1.1e-13  9.96e-01   1.666597934e-07   1.453112874e-07   2.3e-11  0.17
195 3.3e-09  2.8e-11  1.1e-13  1.00e+00   1.663377499e-07   1.450322084e-07   2.3e-11  0.17
196 3.4e-09  2.8e-11  1.1e-13  1.00e+00   1.662827373e-07   1.449844915e-07   2.3e-11  0.17
197 3.4e-09  2.8e-11  1.1e-13  1.00e+00   1.661572204e-07   1.448759085e-07   2.3e-11  0.17
198 3.4e-09  2.8e-11  1.1e-13  1.00e+00   1.661501673e-07   1.448697857e-07   2.3e-11  0.17
199 3.5e-09  2.8e-11  1.1e-13  1.00e+00   1.661463733e-07   1.448664964e-07   2.3e-11  0.17
200 3.5e-09  2.8e-11  1.1e-13  1.00e+00   1.661423548e-07   1.448629987e-07   2.3e-11  0.18
201 3.1e-09  1.6e-11  4.8e-14  9.98e-01   9.867162810e-08   8.628147625e-08   1.4e-11  0.18
202 3.3e-09  1.6e-11  4.8e-14  1.00e+00   9.857836370e-08   8.620011376e-08   1.4e-11  0.18
203 2.9e-09  1.6e-11  4.7e-14  1.00e+00   9.724586113e-08   8.504100334e-08   1.4e-11  0.18
204 3.3e-09  1.6e-11  4.6e-14  1.00e+00   9.640038305e-08   8.430508772e-08   1.3e-11  0.18
205 3.2e-09  1.6e-11  4.5e-14  1.00e+00   9.497575659e-08   8.306525692e-08   1.3e-11  0.18
206 3.3e-09  1.5e-11  4.5e-14  1.00e+00   9.481822284e-08   8.292824109e-08   1.3e-11  0.18
207 3.4e-09  1.5e-11  4.5e-14  1.00e+00   9.460769221e-08   8.274491029e-08   1.3e-11  0.18
208 3.4e-09  1.5e-11  4.5e-14  1.00e+00   9.460753398e-08   8.274476354e-08   1.3e-11  0.18
209 3.2e-09  1.5e-11  4.4e-14  1.00e+00   9.421002515e-08   8.239880774e-08   1.3e-11  0.18
210 3.3e-09  1.5e-11  4.4e-14  1.00e+00   9.338129860e-08   8.167740950e-08   1.3e-11  0.18
211 3.4e-09  1.5e-11  4.4e-14  1.00e+00   9.320759937e-08   8.152600982e-08   1.3e-11  0.19
212 3.4e-09  1.5e-11  4.4e-14  1.00e+00   9.320381115e-08   8.152267393e-08   1.3e-11  0.19
213 3.4e-09  1.5e-11  4.4e-14  1.00e+00   9.320020538e-08   8.151953876e-08   1.3e-11  0.19
214 3.4e-09  1.5e-11  4.4e-14  1.00e+00   9.319913245e-08   8.151859667e-08   1.3e-11  0.19
215 3.5e-09  1.5e-11  4.4e-14  1.00e+00   9.319890211e-08   8.151842679e-08   1.3e-11  0.19
216 3.5e-09  1.5e-11  4.4e-14  1.00e+00   9.319670681e-08   8.151649628e-08   1.3e-11  0.19
217 3.5e-09  1.5e-11  4.4e-14  1.00e+00   9.319670681e-08   8.151649628e-08   1.3e-11  0.19
218 3.5e-09  1.5e-11  4.4e-14  1.00e+00   9.319670681e-08   8.151649628e-08   1.3e-11  0.19
Optimizer terminated. Time: 0.20

ERROR: Solution is not optimal with error code: SLOW_PROGRESS


Moreover, the second issue is still valid for both solvers to my understanding.

It looks like you could just relax some of the tolerances?

The Mosek error is just saying that it is having a hard time closing the remainder of the gap, but the problem and dual solutions are pretty close (1e-8) so you might be satisfied with that solution?

Thanks so much for your support! I have tried changing that gap to 10^{-4} but then I was able to get the same error under different problem settings. The second issue listed above also gave me a positive result for some variable that I believed would be = 0 at optimality. So either I am doing something wrong in my formulation, or one of the solvers/interfaces has a bug.