First steps
Using NLPModels standard modeling interface
NLPModelsAlgencan is naturally built as an NLPModels interface. Hence, one needs an implementation of an AbstractNLPModel to call the Algencan solver.
NLPModelsAlgencan.algencan — Functionoutput = algencan(nlp; kwargs...)
Solves the NLPModel problem nlp using Algencan.
There is a set of optional keywords arguments allowed, see Optional parameters for the list of options accepted.
For instance, the NLPModels package provides an automatic differentiation NLPModel, called ADNLPModel, using ForwardDiff to compute the derivatives. For further details, it is recommended to access this tutorial. As an example, the following optimization problem is defined as:
\[\begin{aligned} \min \quad & f(x_1, x_2) = x_1x_2 + 5 \\ \textrm{s.t.} \quad & x_1+x_2 \leq 5, \\ & x_1^2+x_2^2=10, \\ & 0 \leq x_1, x_2 \leq 5, \end{aligned}\]
And could be modeled as an ADNLModel as follows:
using NLPModels, NLPModelsAlgencan
x0 = [1.0; 1.0]
f(x) = x[1]*x[2] + 5
lvar = [0.0; 0.0]
uvar = [5.0; 5.0]
c(x) = [x[1] + x[2]; x[1]^2 + x[2]^2]
lcon = [-Inf; 10.0]
ucon = [5.0; 10.0]
nlp = ADNLPModel(f, x0, lvar, uvar, c, lcon, ucon)Moreover, it is solved with Algencan and displayed the problem statistics, which is provided by a return instance of a GenericExecutionStats:
stats = algencan(nlp)
print(stats)
==============================================================================
This is ALGENCAN 3.1.1.
ALGENCAN, an Augmented Lagrangian method for nonlinear programming, is part of
the TANGO Project: Trustable Algorithms for Nonlinear General Optimization.
See http://www.ime.usp.br/~egbirgin/tango/ for details.
==============================================================================
There are no strings to be processed in the array of parameters.
The specification file is not being used.
Available HSL subroutines = NONE
ALGENCAN PARAMETERS:
firstde = T
seconde = T
truehpr = T
hptype in TN = TRUEHP
lsslvr in TR = NONE/NONE
lsslvr in NW = NONE/NONE
lsslvr in ACCPROC = NONE/NONE
innslvr = TN
accproc = F
rmfixv = T
slacks = F
scale = T
epsfeas = 1.0000D-08
epsopt = 1.0000D-08
efstain = 1.0000D-04
eostain = 1.0000D-12
efacc = 1.0000D-04
eoacc = 1.0000D-04
iprint = 10
ncomp = 6
Specification filename = ''
Output filename = ''
Solution filename = ''
Number of variables : 2
Number of equality constraints : 1
Number of inequality constraints : 1
Number of bound constraints : 4
Number of fixed variables : 0
There are no fixed variables to be removed.
Objective function scale factor : 1.0D+00
Smallest constraints scale factor : 5.0D-01
Entry to ALGENCAN.
Number of variables : 2
Number of constraints: 2
out penalt objective infeas scaled scaled infeas norm |Grad| inner Newton
ite function ibilty obj-funct infeas +compl graLag infeas totit forKKT
0 6.000D+00 8.D+00 6.000D+00 4.D+00 4.D+00 1.D+00 4.D+00 0 0 0
1 8.D+00 9.867D+00 3.D-01 9.867D+00 1.D-01 1.D-01 1.D-08 3.D-01 5C 0 0
2 1.D+02 1.000D+01 1.D-10 1.000D+01 6.D-11 6.D-11 5.D-11 1.D-10 8C 0 0
Flag of ALGENCAN: Solution was found.
User-provided subroutines calls counters:
Subroutine fsub (coded=F): 0
Subroutine gsub (coded=F): 0
Subroutine hsub (coded=F): 0
Subroutine csub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine jacsub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine hcsub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine fcsub (coded=T): 18
Subroutine gjacsub (coded=T): 16
Subroutine gjacpsub (coded=F): 0
Subroutine hlsub (coded=T): 8
Subroutine hlpsub (coded=F): 0
Total CPU time in seconds = 3.25
Generic Execution stats
status: first-order stationary
objective value: 9.999999999942318
primal feasibility: 1.1536371857800987e-10
dual feasibility: 5.768185928900493e-11
solution: [2.2360679774868917 2.2360679774868917]
multipliers: [0.0 -0.499999999989881]
iterations: -1
elapsed time: 3.292833567Using JuMP modeling interface
Alternatively, one can use the JuMP interface to model the problem and then solve it with Algencan. This solution is provided by the NLPModelsJuMP package. To model the same problem as before, it could be done as follows:
using JuMP, NLPModelsJuMP, NLPModelsAlgencan
model = Model()
@variable(model, 0 ≤ x[1:2] ≤ 5)
set_start_value(x[1], 1.0)
set_start_value(x[2], 1.0)
@NLobjective(model, Min, x[1]*x[2] + 5)
@constraint(model, x[1] + x[2] ≤ 5)
@NLconstraint(model, x[1]^2 + x[2]^2 == 10)
nlp = MathOptNLPModel(model)
stats = algencan(nlp)
print(stats)
==============================================================================
This is ALGENCAN 3.1.1.
ALGENCAN, an Augmented Lagrangian method for nonlinear programming, is part of
the TANGO Project: Trustable Algorithms for Nonlinear General Optimization.
See http://www.ime.usp.br/~egbirgin/tango/ for details.
==============================================================================
There are no strings to be processed in the array of parameters.
The specification file is not being used.
Available HSL subroutines = NONE
ALGENCAN PARAMETERS:
firstde = T
seconde = T
truehpr = T
hptype in TN = TRUEHP
lsslvr in TR = NONE/NONE
lsslvr in NW = NONE/NONE
lsslvr in ACCPROC = NONE/NONE
innslvr = TN
accproc = F
rmfixv = T
slacks = F
scale = T
epsfeas = 1.0000D-08
epsopt = 1.0000D-08
efstain = 1.0000D-04
eostain = 1.0000D-12
efacc = 1.0000D-04
eoacc = 1.0000D-04
iprint = 10
ncomp = 6
Specification filename = ''
Output filename = ''
Solution filename = ''
Number of variables : 2
Number of equality constraints : 1
Number of inequality constraints : 1
Number of bound constraints : 4
Number of fixed variables : 0
There are no fixed variables to be removed.
Objective function scale factor : 1.0D+00
Smallest constraints scale factor : 5.0D-01
Entry to ALGENCAN.
Number of variables : 2
Number of constraints: 2
out penalt objective infeas scaled scaled infeas norm |Grad| inner Newton
ite function ibilty obj-funct infeas +compl graLag infeas totit forKKT
0 6.000D+00 8.D+00 6.000D+00 4.D+00 4.D+00 1.D+00 4.D+00 0 0 0
1 8.D+00 9.867D+00 3.D-01 9.867D+00 1.D-01 1.D-01 1.D-08 3.D-01 5C 0 0
2 1.D+02 1.000D+01 1.D-10 1.000D+01 6.D-11 6.D-11 5.D-11 1.D-10 8C 0 0
Flag of ALGENCAN: Solution was found.
User-provided subroutines calls counters:
Subroutine fsub (coded=F): 0
Subroutine gsub (coded=F): 0
Subroutine hsub (coded=F): 0
Subroutine csub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine jacsub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine hcsub (coded=F): 0 ( 0 calls per constraint in avg)
Subroutine fcsub (coded=T): 18
Subroutine gjacsub (coded=T): 16
Subroutine gjacpsub (coded=F): 0
Subroutine hlsub (coded=T): 8
Subroutine hlpsub (coded=F): 0
Total CPU time in seconds = 2.39
Generic Execution stats
status: first-order stationary
objective value: 9.999999999942318
primal feasibility: 1.1536371857800987e-10
dual feasibility: 5.768185928900493e-11
solution: [2.2360679774868917 2.2360679774868917]
multipliers: [0.0 -0.499999999989881]
iterations: -1
elapsed time: 2.435221733