The Unconstrained Nonlinear Programming Solver

Getting Started

Consider a simple nonlinear problem as follows:

You can formulate and solve the problem by using PROC OPTMODEL as follows:

    proc optmodel;
      var x;
 
      minimize f = sin(x) + cos(x);
 
      solve with nlpu / tech = lbfgs;
 
    quit;
 

A problem summary and a solution summary are displayed in Figure 11.2.

The OPTMODEL Procedure Problem Summary Objective Sense Minimization Objective Function f Objective Type Nonlinear     Number of Variables 1 Bounded Above 0 Bounded Below 0 Bounded Below and Above 0 Free 1 Fixed 0     Number of Constraints 0 The OPTMODEL Procedure Solution Summary Solver L-BFGS Objective Function f Solution Status Optimal Objective Value -1.414213562 Iterations 5     Optimality Error 1.046407E-6

Figure 11.2: Optimal Solution of the Example Problem

The iteration log is shown in Output 11.3.

NOTE: The problem has 1 variables (1 free, 0 fixed). NOTE: The problem has 0 linear constraints (0 LE, 0 EQ, 0 GE, 0 range). NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range). NOTE: Using analytic derivatives for objective. NOTE: The LIMITED MEMORY BFGS solver for unconstrained optimization is called. Objective Optimality Function Iter Value Error Calls 0 1.00000000 1.00000000 1 1 -1.36371237 0.10334611 6 2 -1.41417504 0.00310323 9 3 -1.41421338 0.00021392 12 4 -1.41421356 0.00001495429 15 5 -1.41421356 0.00000104641 18 NOTE: Optimal. NOTE: Objective = -1.41421356.

Figure 11.3: Iteration Log