Optimization problem with lower and upper bounded constraints

maximize:x0.063x4x7 −5.04x1 −0.035x2 −10x3 −3.36x5

subject to: x5 = 1.22x4 −x1

x6 = (98000 x3x4)/(x9 + 1000x3)

x8 = (x2 + x5)/x1

(99/100)x4 ≤x1(1.12 + 0.13167x8 −0.00667x28) ≤(100/99)x4

(99/100)x7 ≤86.35 + 1.098x8 −0.038x28 + 0.325(x6 −89) ≤(100/99)x7

(9/10)x9 ≤35.82 −0.222x10 ≤(10/9)x9

(99/100)x10 ≤−133 + 3x7 ≤(100/99)x10

[0,0,0,0,0,85,90,3,0.01,145] ≤x

x≤[2000,16000,120,5000,2000,93,95,12,4,162]

How do I represent constraints 4 through 6? This is what i have so far:

clc; clear
x = optimvar('x',10,'UpperBound',[2000;16000;120;5000;2000;93;95;12;4;162],"LowerBound",[0;0;0;0;0;85;90;3;0.01;145]);
prob = optimproblem("Objective",0.063*x(4)*x(7)-5.04*x(1)-0.035*x(2)-10*x(3)-3.36*x(5),"ObjectiveSense","maximize")
prob.Constraints.c1 = x(5) == 1.22*x(4)-x(1);
prob.Constraints.c2 = x(6) == 9800* x(3)/(x(4)*x(9)+1000*x(3));
prob.Constraints.c3 = x(8) == (x(2)+x(5))/x(1);
show(prob)

Answer 1

[Walter Roberson]

clc; clear
x = optimvar('x',10,'UpperBound',[2000;16000;120;5000;2000;93;95;12;4;162],"LowerBound",[0;0;0;0;0;85;90;3;0.01;145]);
prob = optimproblem("Objective",0.063*x(4)*x(7)-5.04*x(1)-0.035*x(2)-10*x(3)-3.36*x(5),"ObjectiveSense","maximize")

prob = 
  OptimizationProblem with properties:

       Description: ''
    ObjectiveSense: 'maximize'
         Variables: [1×1 struct] containing 1 OptimizationVariable
         Objective: [1×1 OptimizationExpression]
       Constraints: [0×0 struct] containing 0 OptimizationConstraints

  See problem formulation with show.

prob.Constraints.c1 = x(5) == 1.22*x(4)-x(1);
prob.Constraints.c2 = x(6) == 9800* x(3)/(x(4)*x(9)+1000*x(3));
prob.Constraints.c3 = x(8) == (x(2)+x(5))/x(1);
prob.Constraints.c4 = (99/100)*x(4) <= x(1)*(1.12 + 0.1367*x(8) - 0.00667*x(2)*x(8));
prob.Constraints.c5 = x(1)*(1.12 + 0.1367*x(8) - 0.00667*x(2)*x(8)) <= (100/99)*x(4);
prob.Constraints.c6 = (99/100)*x(7) <= 86.35 + 1.098*x(8) - 0.038*x(2)*x(8) + 0.325*(x(6)-89);
prob.Constraints.c7 = 86.35 + 1.098*x(8) - 0.038*x(2)*x(8) + 0.325*(x(6)-89) <= (100/99)*x(7);

show(prob)

  OptimizationProblem : 

	Solve for:
       x

	maximize :
       0.063*x(4)*x(7) - 5.04*x(1) - 0.035*x(2) - 10*x(3) - 3.36*x(5)


	subject to c1:
       x(1) - 1.22*x(4) + x(5) == 0

	subject to c2:
       x(6) == ((9800 .* x(3)) ./ ((x(4) .* x(9)) + (1000 .* x(3))))

	subject to c3:
       x(8) == ((x(2) + x(5)) ./ x(1))

	subject to c4:
       (0.99 .* x(4)) <= (x(1) .* ((1.12 + (0.1367 .* x(8))) - ((0.00667 .* x(2)) .* x(8))))

	subject to c5:
       (x(1) .* ((1.12 + (0.1367 .* x(8))) - ((0.00667 .* x(2)) .* x(8)))) <= (1.0101 .* x(4))

	subject to c6:
       (0.99 .* x(7)) <= (((86.35 + (1.098 .* x(8))) - ((0.038 .* x(2)) .* x(8))) + (0.325 .* (x(6) - 89)))

	subject to c7:
       (((86.35 + (1.098 .* x(8))) - ((0.038 .* x(2)) .* x(8))) + (0.325 .* (x(6) - 89))) <= (1.0101 .* x(7))

	variable bounds:
          0 <= x(1)  <= 2000
          0 <= x(2)  <= 16000
          0 <= x(3)  <= 120
          0 <= x(4)  <= 5000
          0 <= x(5)  <= 2000
         85 <= x(6)  <= 93
         90 <= x(7)  <= 95
          3 <= x(8)  <= 12
       0.01 <= x(9)  <= 4
        145 <= x(10) <= 162

and so on.

I had to guess about what x28 was; I coded it as x(2)*x(8)

[Anthony Sirico]

Sorry its x^2...so did you break each of them up into 2 separate constraints?

[Walter Roberson]

Yes, split the range inequality into two inequalities.

The x28 cannot be x^2 because x is a vector. Perhaps it is a clumsy x(8)^2