The OPTLSO Procedure

The following optimization problem is discussed in Haverly (1978) and Liebman et al. (1986). This example illustrates how to use PROC FCMP to define nonlinear constraints and use an MPS data set to define linear constraints. Minimize

subject to

and

In the following steps, the linear component of the problem definition is first described in PROC OPTMODEL and then saved as an MPS data set. Because the objective is linear, no FCMP objective function needs to be used. In the second section of steps, the nonlinear constraints are defined by using FCMP functions, and their corresponding names and lower and upper bounds are stored in the data set condata. The OPTLSO procedure is then called with the options NLINCON=CONDATA and MPSDATA=NLCEX.

proc optmodel;  
   var x{1..10} >= 0;
   x[10].lb = 1;
   x[10].ub = 3;
   x[1].ub = 100;
   x[2].ub = 200;
   con x[3] + x[4] = x[6] + x[7],
   x[6] + x[8] = x[1],
   x[7] + x[9] = x[2],
   x[8] + x[9] = x[5];
   max f = 9*x[1] + 15*x[2] - 6*x[3] - 16*x[4] - 10*x[5];
   save mps nlcexOld;
quit;

%lsompsmod(nlcexOld, nlcex);

proc fcmp outlib=sasuser.myfuncs.mypkg;
   function nlc1(x1,x6,x8,x10);       
      return (2.5*x1 - x10*x6 - 2*x8);
   endsub;  
   function nlc2(x2,x7,x9,x10);   
      return (1.5*x2 - x10*x7 - 2*x9);
   endsub;
   function nlc3(x3,x4,x10);    
      return (3*x3 + x4 - x10*(x3 + x4));
   endsub;
run;  

data condata;
   input _id_ $ _lb_ _ub_;
   datalines;
nlc1 0 .
nlc2 0 .
nlc3 0 0
;

options cmplib = sasuser.myfuncs;
proc optlso  
   mpsdata   = nlcex    
   nlincon   = condata
   logfreq   = 10;  
   performance nthreads=2;
run; 

Output 3.6.1 shows the ODS tables that are produced from running these steps.

Output 3.6.2 shows the iteration log from running these steps.