Optimization expression operation not supported

I am trying to code a linear programming optimization problem but defining the constraint is proving a little difficult. The constraint is determined as:

• difference of asset and liabilities cashflows is calculated, and
• then the cumulative net cashflows are compounded by interest rates (element wise).
• each element of the resultant matrix / vector is divided by a constant (53.844) and
• constraint is that each element should be less than or equal to 0.05

I have given my code below but the constraint uses the "cumsum" function, which the problem-based approach doesn't entertain. I have also tried an alternative formulation (shown in the end) to avoid use of cumsum but still I did not had any success.

Please can anyone help to correct the code? Also, it would be useful to know how to formulate this problem in the Solver-based approach. It is the code for setting out the constraint that looks difficult to me.

prices = [99.74 91.22 98.71 103.75 97.15];
cashFlows = [4 5 2.5 5 4; 4 5 2.5 5 4; 4 5 2.5 5 4; 4 5 2.5 5 4; 4 5 102.5 5 4;4 5 0 105 104;4 105 0 0 0; 104 0 0 0 0];
obligations = [5 7 7 6 8 7 20 0]';
nt=size(cashFlows,1)
nb=size(cashFlows,2)
Rates = [0.01; 0.015; 0.017;0.019;0.02;0.025;0.027;0.029];
%Number of bonds available
nBonds = [10;100;20;30;5]
ALM = optimproblem;
bonds = optimvar('bonds',nb,'Type','integer','LowerBound',0,'UpperBound',nBonds);
ALM.ObjectiveSense = 'minimize';
ALM.Objective = prices*bonds;

%Define the constraint
ALM.Constraints.Const1 = (cumsum(cashFlows*bonds-obligations,2).*(1+Rates)')/53.844 <=0.05;
showproblem(ALM)
Solution = solve(ALM);
Solution.bonds = round(Solution.bonds);
Solution.bonds

%Alternative formulation of the constraint to avoid use of cumsum
B = triu(ones(8,5));
C=cashFlows*bonds-obligations;
D=C.*B;
E=sum(D,1);
ALM.Constraints.Const1 = (E.*(1+Rates)')/53.844 <=0.05;

Answer 1

[Matt J]

Maybe this is what you intended,

C=cashFlows*bonds-obligations;
E=C.'*triu(ones(8));
ALM.Constraints.Const1 = (E.*(1+Rates)')/53.844 <=0.05;

Otherwise, it is not clear what the constraint is supposed to be. C is an 8x1 column vector, so cumsum(C,2) along dimension 2 wouldn't really make much sense. It would just leave C unchanged, as in the numeric example below.

>> a=rand(8,1)

a =

    0.4897
    0.3395
    0.9516
    0.9203
    0.0527
    0.7379
    0.2691
    0.4228

>> cumsum(a,2)

ans =

    0.4897
    0.3395
    0.9516
    0.9203
    0.0527
    0.7379
    0.2691
    0.4228

Also, it would be useful to know how to formulate this problem in the Solver-based approach.

That can be done with

prob2struct(ALM)

[L Smith]

Thanks Matt By cumsum I intended to add successive rows/columns to get cumulative cash flows.

Your correction has made the code to work but I am getting zeros as answer. I maybe missing on something or it could be there is no answer. Do you have any suggestions for rectifying this?

(The constraint is intended to ensure that each element in the matrix is less than or equal to 0.05).

[Matt J]

your correction has made the code to work but I am getting zeros as answer

In light of your objective,

ALM.ObjectiveSense = 'minimize';
ALM.Objective = prices*bonds;

it makes a lot of sense to me that prices*bounds will be minimized when all bonds(i)=0.

[L Smith]

Thank you. I managed to figure out. It was just an error in the way I defined the constraint.