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QPSlover.java
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166 lines (143 loc) · 4.34 KB
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package symjava.examples;
import symjava.relational.Eq;
import symjava.symbolic.*;
import symjava.symbolic.utils.AddList;
import symjava.symbolic.utils.JIT;
import symjava.symbolic.utils.Utils;
import static symjava.math.SymMath.*;
import static symjava.symbolic.Symbol.*;
public class QPSlover {
public static void main(String[] args) {
test0();
test1();
test2(); //?
test3(); //?
}
public static void test0() {
/**
* http://www.akiti.ca/QuadProgEx0Constr.html
minimize F = (5/2)x1^2 -2x1x2 -x1x3 + 2x2^2 + 3x2x3 + (5/2)x3^2 + 2x1 - 35x2 - 47x3 + 5
True Solution: (x1,x2,x3) = (3,5,7)
*/
Symbol x1 = new Symbol("x_1");
Symbol x2 = new Symbol("x_2");
Symbol x3 = new Symbol("x_3");
Expr F = 2.5*x1*x1 -2*x1*x2 -x1*x3 + 2*x2*x2 + 3*x2*x3 + 2.5*x3*x3 + 2*x1 - 35*x2 - 47*x3 + 5 ;
System.out.println(F);
Expr[] freeVars = new Expr[]{ x1, x2, x3 };
Eq eq = new Eq(F, C0, freeVars);
System.out.println(eq);
double[] guess = new double[freeVars.length];
NewtonOptimization.solve(eq, guess, 10, 1e-3, false);
//Verifiy:
double[][] A = {
{ 5,-2,-1},
{-2, 4, 3},
{-1, 3, 5},
};
double[] b = {-2,35,47};
double[] x = {0, 0, 0};
Solver.solveCG2(A, b, x);
for(double i : x)
System.out.println(i);
}
public static void test1() {
/**
* http://doc.cgal.org/latest/QP_solver/index.html
minimize x^2 + 4(y-4)^2
subject to
x + y <= 7
-x+2y <=4
x>=0
y>=0
y<=4
Solution (x,y)=(2,3)
*/
Expr f = x*x + 4*(y-4)*(y-4);
Symbols lmd = new Symbols("\\lambda");
Symbols c = new Symbols("c");
AddList addList = new AddList();
addList.add(lmd[1]*( x+y-7+c[1]*c[1] ));
addList.add(lmd[2]*(-x+2*y-4+c[2]*c[2] ));
addList.add(lmd[3]*( x-c[3]*c[3] ));
addList.add(lmd[4]*( y-c[4]*c[4] ));
addList.add(lmd[5]*( y-4+c[5]*c[5] ));
Expr L = f + addList.toExpr();
System.out.println(L);
Expr[] freeVars = Utils.joinArrays(new Expr[]{x, y}, lmd.get(1, 5), c.get(1, 5));
Eq eq = new Eq(L, C0, freeVars);
System.out.println(eq);
double[] guess = new double[freeVars.length];
NewtonOptimization.solve(eq, guess, 10, 1e-3, false);
double xx = guess[0];
double yy = guess[1];
double objValue = JIT.compile(f).apply(xx,yy);
System.out.println("Objective Value = "+objValue); //=8
}
public static void test2() {
/**
* http://doc.cgal.org/latest/QP_solver/index.html
minimize -32y+64
subject to
x + y <= 7
-x+2y <=4
x>=0
y>=0
y<=4
Solution (x,y)=(10/3, 11/3)
*/
Expr f = -32*y+64;
Symbols lmd = new Symbols("\\lambda");
Symbols c = new Symbols("c");
AddList addList = new AddList();
addList.add(lmd[1]*( x+y-7+c[1]*c[1] ));
addList.add(lmd[2]*(-x+2*y-4+c[2]*c[2] ));
addList.add(lmd[3]*( x-c[3]*c[3] ));
addList.add(lmd[4]*( y-c[4]*c[4] ));
addList.add(lmd[5]*( y-4+c[5]*c[5] ));
Expr L = f + addList.toExpr();
System.out.println(L);
Expr[] freeVars = Utils.joinArrays(new Expr[]{x, y}, lmd.get(1, 5), c.get(1, 5));
Eq eq = new Eq(L, C0, freeVars);
System.out.println(eq);
double[] guess = new double[freeVars.length];
NewtonOptimization.solve(eq, guess, 10, 1e-3, false);
double xx = guess[0];
double yy = guess[1];
double objValue = JIT.compile(new Expr[]{x,y},f).apply(xx,yy);
System.out.println("Objective Value = "+objValue); //=-160/3
}
public static void test3() {
/**
* http://doc.cgal.org/latest/QP_solver/index.html
minimize x^2 + 4(y-4)^2
subject to
x + y <= 7
-x+2y <=4
x>=0
y>=0
//y<=4
Solution (x,y)=(2,3)
*/
Expr f = x*x + 4*(y-4)*(y-4);
Symbols lmd = new Symbols("\\lambda");
Symbols c = new Symbols("c");
AddList addList = new AddList();
addList.add(lmd[1]*( x+y-7+c[1]*c[1] ));
addList.add(lmd[2]*(-x+2*y-4+c[2]*c[2] ));
addList.add(lmd[3]*( x-c[3]*c[3] ));
addList.add(lmd[4]*( y-c[4]*c[4] ));
//addList.add(lmd[5]*( y-4+c[5]*c[5] ));
Expr L = f + addList.toExpr();
System.out.println(L);
Expr[] freeVars = Utils.joinArrays(new Expr[]{x, y}, lmd.get(1, 4), c.get(1, 4));
Eq eq = new Eq(L, C0, freeVars);
System.out.println(eq);
double[] guess = new double[freeVars.length];
NewtonOptimization.solve(eq, guess, 10, 1e-3, false);
double xx = guess[0];
double yy = guess[1];
double objValue = JIT.compile(new Expr[]{x,y},f).apply(xx,yy);
System.out.println("Objective Value = "+objValue); //=8
}
}