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How to find KKT conditions using maple for maximiz...

Asked by: Andiguys 25
optimization homework
September 26 2024
0  3

How to find KKT conditions using maple for maximization function with constraint?

Decision variable are k1 and k2.

Attaching sheet:Q_KKT.mw

Loop not executing all value just taking 1st value...

Asked by: Andiguys 25
numeric plotting do-loop
September 19 2024
0  7

Loop is not executing all values just considerinng 1st value of tau0 =0.3.

Also how to plot a 2D graph from the loop result

Attaching sheet with questions in the sheet:
for_loop_question_rec.mw

How to do Parameter setting?...

Asked by: Andiguys 25
solve parameters
September 13 2024
1  2

The attached sheet contains equations H1 to H6 and K1 to K3. What data do I need to modify to ensure that the values of H1 to H6 fall between 0 and 1, and K1 to K3 are negative? The parameter ranges are also given in the sheet. Is there a method to achieve this?

rouhg.mw

How to use for loop? Objective function contain pi...

Asked by: Andiguys 25
syntax plotting optimization
August 26 2024
0  24

How to use for loop in the optimization function? The objective function contain piecewise function, in that case what to do?
Can anyone help me with the syntax? I am attaching the sheet below:
Question_loop.mw

Error in optimization? what parameter should ii ch...

Asked by: Andiguys 25
optimization plotting duplicate-question
August 17 2024
0  1

I'm encountering an error in the optimization process when adding constraints C1 and C2. I've attached the sheet for reference. 

Q4.mw
To obtain a graph similar to the one below, which parameters in the data should I adjust? As you can see in the attached sheet, the graph is concave with respect to tau1 but not tau2. What changes should I make to ensure the graph is also concave with respect to tau2?

Dummy graph:-

Error in optimization? Constraint is not taken in ...

Asked by: Andiguys 25
syntax user-error plotting
August 14 2024
1  12

I am attaching a sheet where i found error in the optimization function. Its not considering constrain C3 and C5 . Can anyone help?
N_7.mw

Also in the plot the tau1 value remain same for the optimal lambda. What parameter in the model can be changed in DATA so that i get dome like structure? 

Unable to solve for w?...

Asked by: Andiguys 25
solve
August 13 2024
1  3

I am attaching the sheet, I want to solve for w or find range of w. 
q1.mw

Issues in using isolating variables from constrain...

Asked by: Andiguys 25
solve assumptions inequality
July 15 2024
0  4

I can't isolate a variable from the constraint and move it to one side of the inequality. For example, it's like having theta <= all other terms. I've tried using the isolate and eval functions, but they aren't producing any results or simplifying the expression. What am I doing wrong?

Attaching sheet below (issue marked yellow in background): N_1.mw 

Minimization of a function...

Asked by: Andiguys 25
syntax piecewise numeric
May 30 2024
1  57

Can anyone helps me with my optimization Problem.  Following are the issues :-

  • I have to minimize the function TRC, i am unable to do. 
  • I am unable to add a constraint with if statement. 
  • Check whether i have represented I1 and I2 with respect to alpha and beta right or wrong

Attaching the sheet below, the background marked in yellow is the problem area. Thankyou

Basic_model.mw

Need to Obtain Bifurcation Points and Bifurcation ...

Asked by: Tamour_Mahwish 0
ode differential-equations bifurcation
April 16 2024
0  0

Hello Everyone;

I need to find the bifurcation point and further bifarcation diagram for the given model. But facing error. Can anybody help to do this? Can you refer some library for bifurcation analysis of ODE's? Code is attched. Thanks in Advance. 

123.mw

 

 

 

 

> 

restart

> 

C_m := 1.0; g_K := 36.0; I_inj := 0; g_L := .3; E_Na := 50.0; E_K := -77.0; E_L := -54.4
> 

alpha_m := (.1*(V-25.0))/(1-exp(-(V-25.0)*(1/10))); beta_m := 4*exp(-V/(18.0)); alpha_h := 0.7e-1*exp(-V/(20.0)); beta_h := 1/(1+exp(-(V-30)*(1/10))); alpha_n := (0.1e-1*(V-10.0))/(1-exp(-(V-10.0)/(10.0))); beta_n := .125*exp(-V/(80.0)); I_Na := g_Na*m^3*h*(V-E_Na); I_K := g_K*n^4*(V-E_K); I_L := g_L*(V-E_L)

.125*exp(-0.1250000000e-1*V)

(1.1)
> 

eq1 := (I_inj-I_Na-I_K-I_L)/C_m; m := alpha_m/(alpha_m+beta_m); n := alpha_n/(alpha_n+beta_n); h := alpha_h/(alpha_h+beta_h)

-16.32000000-1.000000000*g_Na*m^3*h*(V-50.0)-36.00000000*n^4*(V+77.0)-.3000000000*V

 

.1*(V-25.0)/((1-exp(-(1/10)*V+2.500000000))*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V)))

 

0.1e-1*(V-10.0)/((1-exp(-.1000000000*V+1.000000000))*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V)))

 

0.7e-1*exp(-0.5000000000e-1*V)/(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))

(1.2)
> 

bif_eq1 := eq1 = 0;

-16.32000000-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.3600000000e-6*(V-10.0)^4*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000*V = 0

> 

bif_eq2 := diff( eq1, V) = 0;

-0.2100000000e-3*g_Na*(V-25.0)^2*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*exp(-(1/10)*V+2.500000000)/((1-exp(-(1/10)*V+2.500000000))^4*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.2100000000e-3*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(.1/(1-exp(-(1/10)*V+2.500000000))-0.1000000000e-1*(V-25.0)*exp(-(1/10)*V+2.500000000)/(1-exp(-(1/10)*V+2.500000000))^2-.2222222222*exp(-0.5555555556e-1*V))/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^4*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.3500000000e-5*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))+0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)*(V-50.0)*(-0.3500000000e-2*exp(-0.5000000000e-1*V)+(1/10)*exp(-(1/10)*V+3)/(1+exp(-(1/10)*V+3))^2)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3)))^2)-0.7000000000e-4*g_Na*(V-25.0)^3*exp(-0.5000000000e-1*V)/((1-exp(-(1/10)*V+2.500000000))^3*(.1*(V-25.0)/(1-exp(-(1/10)*V+2.500000000))+4*exp(-0.5555555556e-1*V))^3*(0.7e-1*exp(-0.5000000000e-1*V)+1/(1+exp(-(1/10)*V+3))))-0.1440000000e-5*(V-10.0)^3*(V+77.0)/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-6*(V-10.0)^4*(V+77.0)*exp(-.1000000000*V+1.000000000)/((1-exp(-.1000000000*V+1.000000000))^5*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)+0.1440000000e-5*(V-10.0)^4*(V+77.0)*(0.1e-1/(1-exp(-.1000000000*V+1.000000000))-0.1000000000e-2*(V-10.0)*exp(-.1000000000*V+1.000000000)/(1-exp(-.1000000000*V+1.000000000))^2-0.1562500000e-2*exp(-0.1250000000e-1*V))/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^5)-0.3600000000e-6*(V-10.0)^4/((1-exp(-.1000000000*V+1.000000000))^4*(0.1e-1*(V-10.0)/(1-exp(-.1000000000*V+1.000000000))+.125*exp(-0.1250000000e-1*V))^4)-.3000000000 = 0

 

 

 
> 

bif_sol := solve({ bif_eq1,bif_eq2}, {V, g_Na});

Warning, solutions may have been lost

 

 

as the solutions, which are then expressed as the points mu, y via

   

[Back to ODE Powertool Table of Contents]

 

 

LagrangeMultipliers...

Asked by: CaptNnFalcon 20
homework intersection ellipse
March 14 2024
2  2

Hi, I have an homework where I need to find the highest point and the lowest point on an ellipse form by the intersection of two equations wich are 4x-3y+8z=5 and z^2=x^2+y^2 and I have to use the LagrangeMultiplier command. I get how it works but I can't get the correct form. How should I do it ? 

{r} values in eigenvectors ...

Asked by: amoi59 15
linearalgebra eigenvalues eigenvectors
December 21 2023
2  6

Hello everyone,

I'm trying to symbolically diagonalize a 5x5 matrix in Maple. I can determine the eigenvalues for my matrix, but when it comes to evaluating the eigenvectors, Maple gives me the following results:

eigenvalues(A): -a + u, a + u, u, u, u

eigenvectors(A): [a + u, 1, {r}], [-a + u, 1, {r}], [u, 5, {r, r, r, r, r}]

I don't understand why I'm getting {r} in the eigenvectors. How can I display the eigenvectors for my matrix A?

Thank you in advance for your answers !

5x5

 

restartNULL

with(linalg)

[BlockDiagonal, GramSchmidt, JordanBlock, LUdecomp, QRdecomp, Wronskian, addcol, addrow, adj, adjoint, angle, augment, backsub, band, basis, bezout, blockmatrix, charmat, charpoly, cholesky, col, coldim, colspace, colspan, companion, concat, cond, copyinto, crossprod, curl, definite, delcols, delrows, det, diag, diverge, dotprod, eigenvals, eigenvalues, eigenvectors, eigenvects, entermatrix, equal, exponential, extend, ffgausselim, fibonacci, forwardsub, frobenius, gausselim, gaussjord, geneqns, genmatrix, grad, hadamard, hermite, hessian, hilbert, htranspose, ihermite, indexfunc, innerprod, intbasis, inverse, ismith, issimilar, iszero, jacobian, jordan, kernel, laplacian, leastsqrs, linsolve, matadd, matrix, minor, minpoly, mulcol, mulrow, multiply, norm, normalize, nullspace, orthog, permanent, pivot, potential, randmatrix, randvector, rank, ratform, row, rowdim, rowspace, rowspan, rref, scalarmul, singularvals, smith, stackmatrix, submatrix, subvector, sumbasis, swapcol, swaprow, sylvester, toeplitz, trace, transpose, vandermonde, vecpotent, vectdim, vector, wronskian]

 (1.1)

A := Matrix([[0, 1, 0, 0, 0], [(gamma-1)*H-u^2-a^2, (3-gamma)*u, -(gamma-1)*v, -(gamma-1)*w, gamma-1], [-u*v, v, u, 0, 0], [-u*w, w, 0, u, 0], [u*((gamma-2)*H-a^2), H-(gamma-1)*u^2, -(gamma-1)*u*v, -(gamma-1)*u*w, gamma*u]])

Matrix(%id = 18446746202416421574)

(1.2)

eigenvalues(A)

u+(-gamma*u^2-gamma*v^2-gamma*w^2+2*H*gamma-a^2+u^2+v^2+w^2-2*H)^(1/2), u-(-gamma*u^2-gamma*v^2-gamma*w^2+2*H*gamma-a^2+u^2+v^2+w^2-2*H)^(1/2), u, u, u

 (1.3)

V := sqrt(u^2+v^2+w^2)

(u^2+v^2+w^2)^(1/2)

(1.4)

H := (1/2)*V^2+a^2/(gamma-1)

(1/2)*u^2+(1/2)*v^2+(1/2)*w^2+a^2/(gamma-1)

(1.5)

eigenvalues(A)

-a+u, a+u, u, u, u

(1.6)

eigenvectors(A)

[-a+u, 1, {r}], [a+u, 1, {r}], [u, 3, {r, r, r}]

(1.7)

``

Download maps.mw

minimax optimization error and failure...

Asked by: RukevweOyinloye 15
optimization minimize optimization
December 18 2023
1  33

Please help me check why my minmax optimization is not having these errors:

Error, (in minimize/cell/function/multidependence/univariate) 

Error, n should be an integer for integer[n]
Error, (in minimize/cell/function/multidependence/univariate) invalid input: `minimize/continuous` expects its 2nd argument, yFP, to be of type {name, list(name)}, but received `X[4,3]` = -infinity

Error, invalid input: `convert/Array` expects its 1st argument, A, to be of type {Array, Matrix, Vector, array, sequential}, but received 0

my design optimization objective function is to carry out a minimize the maximum assignments from vector B overlap  between any two members in A , such that in vector A all members fall under a group and there is no duplication of membership, further   a member from each group representing the group  is to be assigned to vector B such that only one member of a group should be assigned each member of vector B, while ensuring that every member in vector B has represntation from every group in vector A. 

with(Optimization); num_profiles := 4; num_websites := 3; num_groups := 2; X := Array(1 .. num_profiles, 1 .. num_websites, datatype = integer[0 .. 1]); obj := minimize(max(seq(add(X[i, j], j = 1 .. num_websites), i = 1 .. num_profiles))); constraints := {seq(add(add(X[i, j], i = k*num_profiles/num_groups+1 .. (k+1)*num_profiles/num_groups), k = 0 .. num_groups-1) = 1, j = 1 .. num_websites)}; sol := Optimization[Minimize](obj, constraints, assume = binary); optimal_assignment := convert(sol[1], Array); for i to num_profiles do for j to num_websites do if optimal_assignment[i, j] = 1 then print("Profile ", i, " assigned to Website ", j) end if end do end do; print("Objective Value (Minimized Maximum Website Overlap): ", sol[2])

"Objective Value (Minimized Maximum Website Overlap): ", [obj = 0, X[1, 1] = 0, X[1, 2] = 0, X[1, 3] = 0, X[2, 1] = 0, X[2, 2] = 0, X[2, 3] = 1, X[3, 1] = 1, X[3, 2] = 1, X[3, 3] = 0, X[4, 1] = 0, X[4, 2] = 0, X[4, 3] = 0]

 (1)

``

Download firstworkablecode.mw

Unevaluate Expression...

Asked by: digerdiga 390
typesetting boolean inequality
November 23 2023
1  17

Sorry if this is already known, but I haven't found the proper function call.

I just want to "print" this expression without evaluating the boolean calls

restart;
P(X <= 5) = P(-5 <= -X) = P(E(X) - 5 <= E(X) - X);

As it stands, this will evaluate to "false" which I obviously don't want.

I just want to use it as a displayer.

How do I solve this nonlinear system in Maple?...

Asked by: Dyman 15
solve plotting
November 20 2023
3  10

Hi, I'm trying to solve these 2 nonlinear equations in f, g, and x, where x is from 0 to 1 with an increment of 0.1.

I am new to Maple and do not know the basics. Please try and help me. I'd highly appreciate it.

Since this is a nonlinear system, multiple solutions exist, I need to find the first 3 or 5 solutions. Once I solve the system, I would like to plot 2 plots, y-x and z-x.

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