# [Ipopt] Does Ipopt use Reduce Space Interior Point method?

Mon Feb 9 08:05:04 EST 2015

```Hello Everyone!

I use ipopt 3.11.7 via matlab interface with linear solver ma57
It Seems it solved my problem in 20s, but ipopt cost 18s.
the exact NLP jacobian and hessian function cost 2s.
the problem is a optimal control problem, it was very sparse.
Some research show that Reduce Space Interior Point method can speed  KKT
solving times.

So my question is* Does Ipopt use Reduce Space Interior Point Method*? (not
the kind of reduce space technique to form hessian matrix)
Or it has options to allow to speed up the KKT solving.

If it doesn't, Do you have Any advice to speed up solving my optimal
control problems?

the jacobian matrix size: 2611*(2504+1134)
Nonzeros in jacobian matrix  :   (165616 + 61236)       2.39%
the Hessian matrix size:    2611*2611
Nonzeros in Hessian matrix :   90937                          1.33%

*Here is my Program log as follows：*

This is Ipopt version 3.11.7, running with linear solver ma57.

Number of nonzeros in equality constraint Jacobian...:   165616
Number of nonzeros in inequality constraint Jacobian.:    61236
Number of nonzeros in Lagrangian Hessian.............:    90937

Reallocating memory for MA57: lfact (8124492)
Reallocating memory for MA57: lfact (9949073)
Total number of variables............................:     2611
variables with only lower bounds:        0
variables with lower and upper bounds:      280
variables with only upper bounds:        0
Total number of equality constraints.................:     2504
Total number of inequality constraints...............:     1134
inequality constraints with only lower bounds:        0
inequality constraints with lower and upper bounds:     1134
inequality constraints with only upper bounds:        0

iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
0 1.7160931e+005 4.05e+002 2.22e+001   0.0 0.00e+000    -  0.00e+000
0.00e+000   0
1 1.6394305e+005 3.37e+002 1.80e+001  -0.5 5.54e+000    -  5.08e-001
1.67e-001h  1
2 1.2964367e+005 2.25e-001 2.52e+001  -0.6 3.87e+000    -  7.64e-001
1.00e+000h  1
3 1.3054588e+005 1.63e-001 2.69e+001  -0.1 8.94e-001   0.0 1.00e+000
3.08e-001f  2
4 1.3082580e+005 8.45e-003 1.83e+000  -0.8 3.42e+000    -  9.66e-001
1.00e+000h  1
5 1.3014168e+005 4.09e-003 2.25e-001  -1.8 4.03e-001    -  9.74e-001
1.00e+000f  1
6 1.2985090e+005 7.35e-003 5.45e-001  -7.7 1.16e+000    -  5.83e-001
1.00e+000f  1
7 1.2974092e+005 2.65e-003 1.11e-001  -2.5 1.63e+000    -  9.45e-001
8.20e-001h  1
8 1.2969486e+005 1.36e-003 7.48e-001  -3.1 8.63e-001    -  9.74e-001
6.56e-001h  1
9 1.2966988e+005 1.72e-003 5.80e-001  -3.6 6.38e-001    -  1.00e+000
7.10e-001h  1
iter    objective    inf_pr   inf_du lg(mu)  ||d||  lg(rg) alpha_du
alpha_pr  ls
10 1.2966203e+005 1.11e-003 3.07e-001  -4.5 4.00e-001    -  1.00e+000
7.16e-001h  1
11 1.2966050e+005 4.17e-004 7.80e-002  -5.2 1.79e-001    -  1.00e+000
8.11e-001h  1
Reallocating memory for MA57: lfact (10761429)
12 1.2966060e+005 1.48e-004 4.33e-002  -5.7 3.75e-002    -  1.00e+000
6.48e-001h  1
13 1.2966068e+005 1.29e-005 4.27e-003  -6.8 1.46e-002    -  1.00e+000
9.13e-001h  1
14 1.2966069e+005 4.55e-007 4.26e-006  -7.6 4.24e-003    -  1.00e+000
1.00e+000h  1
15 1.2966069e+005 1.32e-008 1.66e-007  -9.7 7.05e-004    -  1.00e+000
1.00e+000h  1
16 1.2966069e+005 7.92e-011 1.05e-009 -11.0 5.56e-005    -  1.00e+000
1.00e+000h  1

Number of Iterations....: 16

(scaled)                 (unscaled)
Objective...............:  4.6307390708014606e+002   1.2966069398244091e+005
Dual infeasibility......:  1.0450803869017929e-009   2.9262250833250202e-007
Constraint violation....:  7.9200465630258066e-011   7.9200465630258066e-011
Complementarity.........:  5.7463050022030235e-010   1.6089654006168466e-007
Overall NLP error.......:  1.0450803869017929e-009   2.9262250833250202e-007

Number of objective function evaluations             = 18
Number of objective gradient evaluations             = 17
Number of equality constraint evaluations            = 18
Number of inequality constraint evaluations          = 18
Number of equality constraint Jacobian evaluations   = 17
Number of inequality constraint Jacobian evaluations = 17
Number of Lagrangian Hessian evaluations             = 16
Total CPU secs in IPOPT (w/o function evaluations)   =     18.260
Total CPU secs in NLP function evaluations           =      1.791

EXIT: Optimal Solution Found.
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