Homework Answers
Objective function file
Matlab
function f = che(x)
f = 9* x(:,1).^2 -18*x(:,1).*x(:,2)+13*x(:,2).^2-4;
constraint function file Matlab
function [c,ceq] = con1(x)
c =-(x(1)^2 + x(2)^2+2*x(1)- 16);
ceq = [ ];
running file
options = optimoptions(@fmincon,...
'Display','iter','Algorithm','interior-point');
[x,fval] = fmincon(@con1,[3 1],...
[],[],[],[],[],[],@con1,options)
Output
Iter F-count f(x) Feasibility optimality step
0 3 -0.000000e+00 0.000e+00 8.000e+00
1 6 -3.008791e-01 0.000e+00 8.070e+00 3.633e-02
2 9 -1.360036e+02 0.000e+00 2.400e+01 8.210e+00
3 12 -3.963306e+05 0.000e+00 1.222e+03 6.172e+02
4 15 -2.496720e+10 0.000e+00 3.066e+05 1.574e+05
5 18 -3.907357e+16 0.000e+00 3.835e+08 1.975e+08
6 21 -1.526800e+24 0.000e+00 2.397e+12 1.235e+12
Problem appears unbounded.
fmincon stopped because the objective function value is less
than
the default value of the objective function limit and
constraints
are satisfied to within the default value of the constraint
tolerance.
<stopping criteria details>
x =
1.0e+12 *
1.1987 0.2997
fval =
-1.5268e+24
Add Answer to:
Find points satisfying KKT neccessary conditions for the following problem 4.68; check if they are optimum points using...
Find points satisfying KKT neccessary conditions for the following problem; check if they are optimum points using the...
Find points satisfying KKT neccessary conditions for the
following problem; check if they are optimum points using the
graphical method for the two variable problems. Solve with Matlab
or Excel.
Maximize F(r,t) = (r-92+0-8)2 4.75 subject to 102r+t t s5 ,t20
Maximize F(r,t) = (r-92+0-8)2 4.75
subject to 102r+t t s5 ,t20
Find points satisfying the neccessary conditions for the following problem (4.48); check if it is optimum points using...
Find points satisfying the neccessary conditions for the following
problem (4.48); check if it is optimum points using the graphical
method (if possible). plaese solve with Matlab or Excel.
subject to 2x 3x2-10 X1 + X2 + 2x3-4=0 4.48 Minimizef(x,, x) = 9XF + 18x1x2 + 13x1-4 subject to 저 + x + 2x1 = 16
subject to 2x 3x2-10 X1 + X2 + 2x3-4=0 4.48 Minimizef(x,, x) = 9XF + 18x1x2 + 13x1-4 subject to 저 + x +...
Problem 3: Find points satisfying KKT conditions for the following problem; check if they are opt...
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By using Karush–Kuhn–Tucker (KKT) Conditions and condition for lamda solve the example: We were unable to...
By using Karush–Kuhn–Tucker (KKT) Conditions and condition for
lamda solve the example:
We were unable to transcribe this imageExample: Consider the constrained minimization problem: 2 4 3 min xi + X2 VER? 2 8 subject to 1- Xı – x2 > 0 1- xy + x, 20 1+ x - x2 > 0 1+x+x, 20.
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Name.... * an10 a) Solve...
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Name.... * an10 a) Solve...
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a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
Find points satisfying KKT neccessary conditions for the
following problem; check if they are optimum points using the
graphical method for the two variable problems. Solve with Matlab
or Excel.
Maximize F(r,t) = (r-92+0-8)2 4.75 subject to 102r+t t s5 ,t20
Maximize F(r,t) = (r-92+0-8)2 4.75
subject to 102r+t t s5 ,t20
Find points satisfying the neccessary conditions for the following
problem (4.48); check if it is optimum points using the graphical
method (if possible). plaese solve with Matlab or Excel.
subject to 2x 3x2-10 X1 + X2 + 2x3-4=0 4.48 Minimizef(x,, x) = 9XF + 18x1x2 + 13x1-4 subject to 저 + x + 2x1 = 16
subject to 2x 3x2-10 X1 + X2 + 2x3-4=0 4.48 Minimizef(x,, x) = 9XF + 18x1x2 + 13x1-4 subject to 저 + x +...
Problem 3: Find points satisfying KKT conditions for the following problem; check if they are optimum points if possible. Minimize f(1,2xx2-2x1 -2x2 +2 subject to x1+X2-4-0
Problem 3: Find points satisfying KKT conditions for the following problem; check if they are optimum points if possible. Minimize f(1,2xx2-2x1 -2x2 +2 subject to x1+X2-4-0
By using Karush–Kuhn–Tucker (KKT) Conditions and condition for
lamda solve the example:
We were unable to transcribe this imageExample: Consider the constrained minimization problem: 2 4 3 min xi + X2 VER? 2 8 subject to 1- Xı – x2 > 0 1- xy + x, 20 1+ x - x2 > 0 1+x+x, 20.
4. (40%) using the graphical method find the solution for the following problem. Verify this solution using the KKT requirements. Plot the gradients of the objective function and the active constraints at the optimal point MinfcX,y)- (x-3)2 (Y-3) s.t 9:X+2Y-6s 92: 2X+Y-6s0
4. (40%) using the graphical method find the solution for the following problem. Verify this solution using the KKT requirements. Plot the gradients of the objective function and the active constraints at the optimal point MinfcX,y)- (x-3)2 (Y-3)...
(45 Points) Consider the constrained optimization problem: min f(x1, x2) = 2x} + 9x2 + 9x2 - 6x1x2 – 18x1 X1 X2 Subject to 4x1 – 3x2 s 20 X1 + 2x2 < 10 -X1 < 0, - x2 < 0 a) Is this problem convex? Justify your answer. (5 Points) b) Form the Lagrange function. (5 Points) c) Formulate KKT conditions. (10 Points) d) Recall that one technique for finding roots of KKT condition is to check all permutations...
a) Solve the following problem using graphical method (using the following graph): Minimize f(x,y) - 2x-y subject to the constraints x2+y's 20 y<x (1) (2) (In the space provided below the graph, please write down your solution clearly) we wish to solve the above problem using Exterior Penalty Function approach. Define b) Suppose augmented cost function and explain how to use it to find a solution to the above problem.
a) Solve the following problem using graphical method (using the...
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Name.... * an10 a) Solve...
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Name.... * an10 a) Solve...
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a) Solve the following problem using Lagrange multiplier method. Minimize fCX)-x1+ x2+X 4. subject to: x2+x-3 X1+3x2+ 2x)- 7 (1) (2) (Note: Please do...
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