## Solving NLP Problems With Several Local Minima (nlps5)

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/*               S A S   S A M P L E   L I B R A R Y                */
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/*    NAME: nlps5                                                   */
/*   TITLE: Solving NLP Problems With Several Local Minima (nlps5)  */
/* PRODUCT: OR                                                      */
/*  SYSTEM: ALL                                                     */
/*    KEYS: OR                                                      */
/*   PROCS: OPTMODEL                                                */
/*    DATA:                                                         */
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/* 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;