Optimization expression operation not supported

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L Smith
L Smith 2019-9-16
评论： L Smith 2019-9-17
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;

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采纳的回答

Matt J
Matt J 2019-9-17
编辑：Matt J 2019-9-17
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)
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Matt J
Matt J 2019-9-17
编辑：Matt J 2019-9-17
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
L Smith 2019-9-17
Thank you. I managed to figure out. It was just an error in the way I defined the constraint.

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