# SLOW\_PROGRESS error and an unusual bug

**URL:** <https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700>\
**Category:** Optimization (Mathematical)\
**Created:** [July 17, 2023, 6:03pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700 "2023-07-17T18:03:36Z")\
**Posts on this page:** 5\
**Page:** 1

<div class="post-metadata">

**Author:** ![selvi-aras](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/selvi-aras/32/50637_2.png) [@selvi-aras](https://discourse.julialang.org/u/selvi-aras)\
**Post date:** [July 17, 2023, 6:03pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700/1 "2023-07-17T18:03:36Z")

</div>

Dear JuMP Community,

I have [previously](https://discourse.julialang.org/t/huber-regression-by-using-jump-and-optimizing-with-mosek/100081) 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:

```julia
"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:

```julia
@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](https://discourse.julialang.org/uploads/short-url/pEjDkt3YHTLbaTy9MvctbJyyiEA.jl) (2.5 KB)  
[main\_test.jl](https://discourse.julialang.org/uploads/short-url/AvklIwqvkP2LbYiUofnuF17CJkv.jl) (610 Bytes)

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [July 20, 2023, 7:50pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700/2 "2023-07-20T19:50:25Z")

</div>

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

```plaintext
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

```

---

<div class="post-metadata">

**Author:** ![selvi-aras](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/selvi-aras/32/50637_2.png) [@selvi-aras](https://discourse.julialang.org/u/selvi-aras)\
**Post date:** [July 20, 2023, 8:18pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700/3 "2023-07-20T20:18:22Z")

</div>

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

```julia
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.

---

<div class="post-metadata">

**Author:** ![odow](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/odow/32/28685_2.png) [@odow](https://discourse.julialang.org/u/odow)\
**Post date:** [July 20, 2023, 8:34pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700/4 "2023-07-20T20:34:35Z")

</div>

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?

---

<div class="post-metadata">

**Author:** ![selvi-aras](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/selvi-aras/32/50637_2.png) [@selvi-aras](https://discourse.julialang.org/u/selvi-aras)\
**Post date:** [July 20, 2023, 8:51pm UTC](https://discourse.julialang.org/t/slow-progress-error-and-an-unusual-bug/101700/5 "2023-07-20T20:51:31Z")

</div>

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.