Although the NLP techniques are suited for solving generally constrained nonlinear optimization problems, these techniques can also be used to solve unconstrained and boundconstrained problems efficiently. This example considers the relatively large nonlinear optimization problems

and

with . These problems are unconstrained and boundconstrained, respectively.
For largescale problems, the default memory limit might be too small, which can lead to outofmemory status. To prevent this occurrence, it is recommended that you set a larger memory size. See the section Memory Limit for more information.
To solve the first problem, you can write the following statements:
proc optmodel; number N=100000; var x{1..N} init 1.0; minimize f = sum {i in 1..N  1} (4 * x[i] + 3.0) + sum {i in 1..N  1} (x[i]^2 + x[N]^2)^2; solve with nlp; quit;
The problem and solution summaries are shown in Output 8.2.1.
Output 8.2.1: Problem Summary and Solution Summary
Problem Summary  

Objective Sense  Minimization 
Objective Function  f 
Objective Type  Nonlinear 
Number of Variables  100000 
Bounded Above  0 
Bounded Below  0 
Bounded Below and Above  0 
Free  100000 
Fixed  0 
Number of Constraints  0 
Performance Information  

Execution Mode  On Client 
Number of Threads  2 
Solution Summary  

Solver  NLP 
Algorithm  Interior Point 
Objective Function  f 
Solution Status  Optimal 
Objective Value  0 
Iterations  16 
Optimality Error  1.007903E14 
Infeasibility  0 
To solve the second problem, you can write the following statements (here the activeset method is specifically selected):
proc optmodel; number N=100000; var x{1..N} >= 1 <= 2; minimize f = sum {i in 1..N  1} cos(0.5*x[i+1]  x[i]^2); solve with nlp / algorithm=activeset; quit;
The problem and solution summaries are shown in Output 8.2.2.
Output 8.2.2: Problem Summary and Solution Summary
Problem Summary  

Objective Sense  Minimization 
Objective Function  f 
Objective Type  Nonlinear 
Number of Variables  100000 
Bounded Above  0 
Bounded Below  0 
Bounded Below and Above  100000 
Free  0 
Fixed  0 
Number of Constraints  0 
Performance Information  

Execution Mode  On Client 
Number of Threads  2 
Solution Summary  

Solver  NLP 
Algorithm  Active Set 
Objective Function  f 
Solution Status  Optimal 
Objective Value  99999 
Iterations  12 
Optimality Error  1.449048E12 
Infeasibility  0 