# How to use qld function without the error message **URL:** \ **Category:** Optimization\ **Created:** [March 18, 2024, 2:15pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432 "2024-03-18T14:15:32Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![FUJIMOTO](https://avatars.discourse-cdn.com/v4/letter/f/eb8c5e/32.png) [@FUJIMOTO](https://scilab.discourse.group/u/FUJIMOTO)\ **Post date:** [March 18, 2024, 2:15pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/1 "2024-03-18T14:15:32Z")
I have a convex polyhedral cone defined as \{Ax,x\geq 0\}. I want to determine whether a point y lies in this cone. To do so, I solve the following linear programming problem: \begin{align\*} \operatorname{Minimize}&: (x\_1 + x\_2 + ...+ x\_n) \\ \text{Subject to}&:\\ x &\geq 0,\\ y - Ax &= 0. \end{align\*} The existence of a feasible solution in the linear programming problem is equivalent to y belongs to the convex polyhedral cone \{Ax,x\geq 0\}. The point y = (-1, -1)^\top is not a point in the convex polyhedral cone when A = I. Solving the Linear Programming Problem: Let’s solve the following linear programming problem: ```Scilab Q=zeros(2,2); p=[1;1]; b=-[1;1]; C=eye(2,2); ci=[0;0]; cs=[]; me=2; [x ,lagr ,info] = qld(Q, p, C, b, ci, cs, me ) ``` However, it currently stops with the error message: ```auto qld: The constraints are inconsistent. ``` Desired Outcome: I expect the solver to return info == 10 and I want to continue the conditional branches based on the value of info. How can I proceed the code without the error message and stopping the execution? ---
**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\ **Post date:** [March 18, 2024, 3:01pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/2 "2024-03-18T15:01:59Z")
Hello, You are right, when 3 output arguments are provided no error should be raised, can you create an issue at [Issues · scilab / scilab · GitLab](https://gitlab.com/scilab/scilab/-/issues) ? In the meantime, if you just need an information on feasibility, could you use karmarkar ([karmarkar - Solves a linear optimization problem.](https://help.scilab.org/karmarkar)) ? ```Scilab p=[1;1] b=-[1;1] A=eye(2,2); [xopt,fopt,exitflag]=karmarkar(A,b,p); exitflag --> exitflag exitflag = -1. ``` -1 means no feasible solution. S. ---
**Author:** ![FUJIMOTO](https://avatars.discourse-cdn.com/v4/letter/f/eb8c5e/32.png) [@FUJIMOTO](https://scilab.discourse.group/u/FUJIMOTO)\ **Post date:** [March 19, 2024, 7:31am UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/3 "2024-03-19T07:31:00Z")
Mr. mottelet. I greatly appreciate your advice ! When I ran the simulation karmarkar worked fine for many parameters, but I got error messages “karmarkar: Wrong value for input argument #4. x0 does not satisfy the equality constraints.” for the following parameters.Is there a solution to avoid the error? Aeq=[ 1,1,-1,-1,0; 0,1,1,0,-1; -1,-1,-1,-1,-1 ] beq=[ 0; 1; -1 ] f=[1,1,1,1,1] [xopt,fopt,exitflag]=karmarkar(Aeq,beq,f) ---
**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\ **Post date:** [March 19, 2024, 8:21am UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/4 "2024-03-19T08:21:17Z")
To solve your feasibiity problem (until qld is fixed, likely in next version of Scilab), you can use qp\_solve (not qpsolve, which cannot work in silent mode). Since qp\_solve does not accept bounds you just have to reshape the x\geq 0 constraint as a general linear constraint. For example in the above case ```scilab A = [1,1,-1,-1,0; 0,1,1,0,-1; -1,-1,-1,-1,-1]; y = [0;1;-1]; [m,n] = size(A); Q = eye(n,n); p = zeros(n,1); C = [A;eye(n,n)]'; b = [y;zeros(n,1)]; [x,i,iter,f,info] = qp_solve(Q,p,C,b,m) ``` you get the minimum norm positive x and info==0: ```auto x = 1.850D-17 0.5000000 0.5 5.136D-34 -3.772D-33 i = 2. 8. 1. 7. 3. 0. 0. 0. iter = 6. 0. f = 0.25 info = 0. ``` and for the trivial case you gave at the begining of the topic: ```scilab A = eye(2,2); y = [-1;-1]; [m,n] = size(A); Q = eye(n,n); p = zeros(n,1); C = [A;eye(n,n)]'; b = [y;zeros(n,1)]; [x,i,iter,f,info] = qp_solve(Q,p,C,b,m) ``` you get a warning and info==1: ```auto qp_solve: Warning: The minimization problem has no solution. The results may be inaccurate. x = -1. -1. i = 1. 2. 0. 0. iter = 3. 0. f = 1. info = 1. ``` ---
**Author:** ![FUJIMOTO](https://avatars.discourse-cdn.com/v4/letter/f/eb8c5e/32.png) [@FUJIMOTO](https://scilab.discourse.group/u/FUJIMOTO)\ **Post date:** [March 19, 2024, 10:01am UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/5 "2024-03-19T10:01:44Z")
Dear Stephen, I execute your suggested code.But I have error message as follows: “karmarkar: Wrong value for input argument #4. x0 is not positive.” ---
**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\ **Post date:** [March 19, 2024, 10:12am UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/6 "2024-03-19T10:12:06Z")
karmarkar seems also broken (see [karmarkar fails solving trivial problem (#17227) · Issues · scilab / scilab · GitLab](https://gitlab.com/scilab/scilab/-/issues/17227)), use qp\_solve instead (see my above answer). S. ---
**Author:** ![FUJIMOTO](https://avatars.discourse-cdn.com/v4/letter/f/eb8c5e/32.png) [@FUJIMOTO](https://scilab.discourse.group/u/FUJIMOTO)\ **Post date:** [March 19, 2024, 3:16pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/7 "2024-03-19T15:16:17Z")
Dear mottelet, Thanks a lot to your reply. I could run the simulation successfully. But whenever an infeasible solution is found, I receive warning messages: “qp\_solve: Warning: The minimization problem has no solution. The results may be inaccurate.” Is there any way not to display this message? ---
**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\ **Post date:** [March 19, 2024, 3:17pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/8 "2024-03-19T15:17:17Z")
You can suppress the warnings with: ```scilab warning("off") ``` S. ---
**Author:** ![FUJIMOTO](https://avatars.discourse-cdn.com/v4/letter/f/eb8c5e/32.png) [@FUJIMOTO](https://scilab.discourse.group/u/FUJIMOTO)\ **Post date:** [March 23, 2024, 2:17pm UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/9 "2024-03-23T14:17:42Z")
I think the description of the matrix C in the help file of `qp_solve` is incorrect. The help file suggests multiplying matrix C from the left by an `n`-dimensional column vector `x`, x^\top C(:,j)=b(j) but the dimensions of `x` and the number of rows in `C` (which is `me+md`) do not match. When I set up `C` as per the help file, > C = [A;eye(n,n)]’ //same as help instruction I encountered the following error: > qp\_solve: Wrong value for input argument #5: me must be an integer in the range 0 to 2. I believe the correct formula involves multiplying `x` from the right. C(:,j)x=b(j) and right code according to this interpretation > C = [A;eye(n,n)] However, I received a different error message. > qp\_solve: Wrong value for input argument #5: me must be an integer in the range 0 to 2. Since the number of columns in `C` is 2, there shouldn’t be an error, but I can’t figure out the cause.Please tell me a solution. ```auto A =[1,1;2,1;3,2;4,1] y = [5;2;3;2]; [m,n] = size(A); Q = eye(n,n); p = zeros(n,1); C = [A;eye(n,n)]' //same as help instruction //C = [A;eye(n,n)]; //right formula disp("size(C)",size(C)) b = [y;zeros(n,1)]; [x,i,iter,f,info] = qp_solve(Q,p,C,b,m) disp(info) ``` ---
**Author:** ![mottelet](https://yyz2.discourse-cdn.com/free1/user_avatar/scilab.discourse.group/mottelet/32/13_2.png) [@mottelet](https://scilab.discourse.group/u/mottelet)\ **Post date:** [March 25, 2024, 8:23am UTC](https://scilab.discourse.group/t/how-to-use-qld-function-without-the-error-message/432/10 "2024-03-25T08:23:33Z")
Hello, In an optimisation problem you cannot have more equalities constraints than the dimension of the unknown, which is 2 in your case (2 non redundant equality constraints already uniquely determine the solution). That’s why qld complains. When there are less generating vectors that the dimension of the space, testing wether a given vector is in the cone cannot be made with a linear program. If I understand your example, the cone \mathcal{C} you are considering is a subset of \mathbb{R}^4 since y=(5,2,3,2)^\top and is generated as the positive span of vectors a\_1=(1,2,3,4)^\top,\quad a\_2=(1,1,2,1)^\top. In that case you have less generating vectors (2) than the dimension of the space (4), so testing weither y is a positive combination of these two vectors should be made first by verifying that y is actually in \operatorname{span (a\_1,a\_2)}. For example you can check the rank of matrix (a\_1,a\_2,y): ```scilab -> M = [1 2 3 4;1 1 2 1;5 2 3 2]' M = 1. 1. 5. 2. 1. 2. 3. 2. 3. 4. 1. 2. --> rank(M) ans = 3. ``` here the rank is 3 so y is not a combination of a\_1 and a\_2, hence does not belong to the cone. If we test another vector, e.g. z=(2,3,5,5)^\top, we have ```scilab --> M = [1 2 3 4;1 1 2 1;2 3 5 5]' M = 1. 1. 2. 2. 1. 3. 3. 2. 5. 4. 1. 5. --> rank(M) ans = 2. ``` hence z belongs to \operatorname{span (a\_1,a\_2)} and the coefficients are uniquely obtained with ```scilab --> [1 2 3 4;1 1 2 1]'\[2 3 5 5]' ans = 1.0000000 1.0000000 ``` S.