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Catenary - Solving a QCQP

Description
This model finds the shape of a hanging chain by minimizing its potential energy.

Source Files
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xbcatena.java

/********************************************************
* BCL Example Problems
* ====================
*
* file xbcatena.java
* 
* QCQP problem (linear objective, convex quadratic constraints)
* Based on AMPL model catenary.mod
* (Source: http://www.orfe.princeton.edu/~rvdb/ampl/nlmodels/ )
*
* This model finds the shape of a hanging chain by
* minimizing its potential energy.
*
* (c) 2008-2024 Fair Isaac Corporation
* author: S.Heipcke, June 2008, rev. Mar. 2011
********************************************************/

import com.dashoptimization.*;
import java.io.*;

public class xbcatena {
static final int N = 100; // Number of chainlinks
static final int L = 1; // Difference in x-coordinates of endlinks

static final double H = 2.0 * L / N; // Length of each link

public static void main(String[] args) throws IOException {
try (XPRBprob prob = new XPRBprob("catenary"); // Initialize BCL and create a new problem
XPRBexprContext context =
new XPRBexprContext() /* Release XPRBexpr instances at end of block. */) {
int i;
XPRBvar[] x, y; // x-/y-coordinates of endpoints of chainlinks
XPRBexpr qe;
XPRBctr cobj, c;

/**** VARIABLES ****/
x = new XPRBvar[N + 1];
for (i = 0; i <= N; i++)
x[i] = prob.newVar("x(" + i + ")", XPRB.PL, -XPRB.INFINITY, XPRB.INFINITY);
y = new XPRBvar[N + 1];
for (i = 0; i <= N; i++)
y[i] = prob.newVar("y(" + i + ")", XPRB.PL, -XPRB.INFINITY, XPRB.INFINITY);
// Bounds: positions of endpoints
// Left anchor
x[0].fix(0);
y[0].fix(0);
// Right anchor
x[N].fix(L);
y[N].fix(0);

/****OBJECTIVE****/
/* Minimise the potential energy:  sum(j in 1..N) (y(j-1)+y(j))/2  */
qe = new XPRBexpr();
cobj = prob.newCtr("Obj", qe.mul(0.5));
prob.setObj(cobj); // Set objective function

/**** CONSTRAINTS ****/
forall(j in 1..N) (x(j)-x(j-1))^2+(y(j)-y(j-1))^2 <= H^2  */
for (i = 1; i <= N; i++)
prob.newCtr(

/****SOLVING + OUTPUT****/
prob.setSense(XPRB.MINIM); // Choose the sense of optimization

/* Problem printing and matrix output: */
/*
prob.print();
prob.exportProb(XPRB.MPS, "catenary");
prob.exportProb(XPRB.LP, "catenary");
*/

/* Start values:
for(i=0;i<=N;i++) x[j].setInitval(j*L/N);
for(i=0;i<=N;i++) y[j].setInitval(0);
*/

prob.lpOptimize(""); // Solve the problem

System.out.println("Solution: " + prob.getObjVal());
for (i = 0; i <= N; i++) System.out.println(i + ": " + x[i].getSol() + ", " + y[i].getSol());
}
}
}