5.8.2. Modeling and Optimization Based on MAPL

In this section, we will use MindOpt APL to model and call MindOpt to solve the problem in Example of Non-linear Programming.

You can refer to the section MindOpt APL for more details. For detailed syntax on using MindOpt APL, please refer to User Manual.

First, create a .mapl file and declare the variables to be optimized.

var x;
var y;
var z;

Declare the objective function

minimize ln(1+exp(x+2*y+z)) + ln(1+exp(x-y-z)) + ln(1+exp(-3*x+y-z)) + ln(1+exp(3*x+z));

Declare the constraints

subto x^2 + y^2 <= 1;

Then, run the solving command, which will automatically build the optimization model and call MindOpt for solving.

solve;

The log of the MindOpt solving process is as follows.

MindOpt Version 2.1.0 (Build date: xxxxxxxx)

Start license validation (current time : xxxxxxxx xx:xx:xx).
License validation terminated. Time : 0.002s

wantsol=1
Model summary.
 - Num. variables     : 3
 - Num. constraints   : 1
 - Num. nonzeros      : 8
 - Bound range        : [1.00e+00,1.00e+00]

Interior point method started.
 Iter         PrimObj         DualObj PrimFea DualFea  GapFea      Mu   Time
    0 +2.77258874e+00 +3.77258875e+00 0.0e+00 1.0e+00 1.0e+00 1.0e+00   0.00s
    1 +2.10107174e+00 +2.23028984e+00 0.0e+00 7.8e-01 1.0e-01 1.0e-01   0.00s
    2 +1.42075610e+00 +1.52543264e+00 6.7e-01 2.7e-01 1.8e-03 1.8e-03   0.00s
    3 +1.65885758e+00 +1.72802441e+00 0.0e+00 1.2e-01 3.6e-02 3.6e-02   0.00s
    4 +1.65511048e+00 +1.69576276e+00 0.0e+00 6.6e-02 2.1e-02 2.1e-02   0.00s
    5 +1.65736811e+00 +1.66000850e+00 0.0e+00 2.6e-04 2.6e-03 2.6e-03   0.00s
    6 +1.65490062e+00 +1.65506485e+00 0.0e+00 9.0e-06 1.6e-04 1.6e-04   0.00s
    7 +1.65474536e+00 +1.65474726e+00 0.0e+00 3.6e-08 1.9e-06 1.9e-06   0.00s
    8 +1.65474358e+00 +1.65474367e+00 0.0e+00 4.9e-12 9.1e-08 9.1e-08   0.00s
Terminated.
 - Method             : Interior point method.
 - Primal objective   : 1.6547435766246e+00
 - Dual objective     : 1.6547436675411e+00
 - Num. threads       : 1
 - Num. iterations    : 8
 - Solver details     : Solver terminated with a primal/dual optimal status.
Interior point method terminated. Time : 0.003883s

Optimizer summary.
 - Optimizer used     : Interior point method
 - Optimizer status   : OPTIMAL

Solution summary.       Primal solution 
 - Objective          : +1.6547435766e+00

OPTIMAL; objective 1.654744
Completed.

Upon successful solving, MindOpt APL will obtain the optimal solution to the problem. We can print it out to view:

print "x={}" % x;
print "y={}" % y;
print "z={}" % z;

The output of the above command is

x = -0.5728551903261085
y = -0.8196564705817261
z = 1.2728750741453017

We can also calculate the corresponding optimal objective function value based on the obtained optimal solution (keeping three decimal places here).

param obj = ln(1+exp(x+2*y+z)) + ln(1+exp(x-y-z)) + ln(1+exp(-3*x+y-z)) + ln(1+exp(3*x+z));
print "obj={:.3f}" % obj;

The output of the above code is as follows:

obj=1.655

The example MAPLLR.mapl provides the complete MindOpt APL source code.

# Example: 2D Regularized Logistic Regression Classifcation
# 
# data points: 
# - label=1: {(1,2), (3,0)}
# - label=-1: {(-1,1),(3,-1)}

var x;
var y;
var z;

minimize ln(1+exp(x+2*y+z)) + ln(1+exp(x-y-z)) + ln(1+exp(-3*x+y-z)) + ln(1+exp(3*x+z));

subto x^2 + y^2 <= 1;

solve;

print "x={}" % x;
print "y={}" % y;
print "z={}" % z;

param obj = ln(1+exp(x+2*y+z)) + ln(1+exp(x-y-z)) + ln(1+exp(-3*x+y-z)) + ln(1+exp(3*x+z));
print "obj={:.3f}" % obj;