Solving NLP Problems With Several Local Minima (nlps5)
/********************************************************************/
/* */
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: nlps5 */
/* TITLE: Solving NLP Problems With Several Local Minima (nlps5) */
/* PRODUCT: OR */
/* SYSTEM: ALL */
/* KEYS: OR */
/* PROCS: OPTMODEL */
/* DATA: */
/* */
/* SUPPORT: UPDATE: */
/* REF: */
/* MISC: Example 5 from the Nonlinear Programming Solver */
/* chapter of Mathematical Programming. */
/* */
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proc optmodel;
var x{i in 1..5} >= -5 <= 5 init -2;
min f=(x[1] - 1)^2 + (x[1] - x[2])^2 + (x[2] - x[3])^3 +
(x[3] - x[4])^4 + (x[4] - x[5])^4;
con g1: x[1] + x[2]^2 + x[3]^3 = 2 + 3*sqrt(2);
con g2: x[2] + x[4] - x[3]^2 = -2 + 2*sqrt(2);
con g3: x[1]*x[5] = 2;
performance nthreads=4;
solve with nlp/multistart seed=1234 msmaxstarts=10;
print x.init x.msinit x;
quit;
proc optmodel;
var x{i in 1..5} >= -5 <= 5 init -2;
min f=(x[1] - 1)^2 + (x[1] - x[2])^2 + (x[2] - x[3])^3 +
(x[3] - x[4])^4 + (x[4] - x[5])^4;
con g1: x[1] + x[2]^2 + x[3]^3 = 2 + 3*sqrt(2);
con g2: x[2] + x[4] - x[3]^2 = -2 + 2*sqrt(2);
con g3: x[1]*x[5] = 2;
performance nodes=4 nthreads=4;
solve with nlp/multistart seed=1234 msmaxstarts=10;
print x;
quit;