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power and factorial in YALMIP
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TOPIC: power and factorial in YALMIP
#5819
power and factorial in YALMIP 1 Year, 7 Months ago Karma: 0
Hi My Friends,

I am new to YALMIP and have just gotten a question:
Suppose x is a regular column vector in Matlab and m is of type intvar(1,1), then the following two operation are invalid:
1. x.^m
2. factorial(m)

Could anyone tell me how to overcome these? Thanks in advance!

Best,
Paul
partingale
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#5820
Re: power and factorial in YALMIP 1 Year, 7 Months ago Karma: 32
There is no simple way to encode this in a mixed-integer framework, hence not supported in YALMIP.

The only way I can think of is using implies, assuming m only takes small values

F =[]
xtothepowerofm = sdpvar(n,1);
for i = 1:length(x)
for j = mlowerbound:mupperbound
F = [F,implies(m==j,xtothepowerofm(i)==x(i)^j;
end
end

and similiar for factorial
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#5821
Re: power and factorial in YALMIP 1 Year, 7 Months ago Karma: 32
or alternatively by using variable indices and a pre-defined table

here m allowed from 1 to 5
Code:

x = [1;2;3;4]
table = (repmat(x,1,5).^repmat([1 2 3 4 5],length(x),1))
table = double2sdpvar(table);
intvar m
solvesdp([],abs(table(2,m)-8))
double(m)


should return m=3, since x(2)^3 = 8

don't know which model is more efficient
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Last Edit: 2011/10/20 07:56 By lofberg.
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#5822
Re: power and factorial in YALMIP 1 Year, 7 Months ago Karma: 0
Hi Lofberg:

Thank you for the reply.

You inspired to try the element by element approach for the first problem. In particular, to realize x.^m, we can use the following:

for i=1:length(x)
x(i)=x(i)^m;
end

But the factorial is still a trouble, because it involves direct operation on m.

Best,
Paul
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#5823
Re: power and factorial in YALMIP 1 Year, 7 Months ago Karma: 32
How do you intend to solve the problem?

The approch you use will probably kill any chance of solving the problem efficiently (i.e. using a MILP solver). By using the table approach, you get a MILP-representable model (assuming your other constraints and objective are easy)

Factorial can probably only be implemented using a look-up table approach as I coded above. How does the factorial expression enter your model? If it enters in a convex may ( etc + m! < etc), you can implemente it more efficiently using linear constraints
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Last Edit: 2011/10/20 10:37 By lofberg.
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#5824
Re: power and factorial in YALMIP 1 Year, 7 Months ago Karma: 32
BTW, the code you proposed does not work if x is a double and m is a sdpvar, due to a "bug" in MATLAB
users.isy.liu.se/johanl/yalmip/pmwiki.ph...ain.FAQ#QQuestions48

Hence, the possible approaches are
Code:

x = double2sdpvar([1;2;3]);
sdpvar m
for i=1:length(x)
x(i)=x(i)^m;
end


or
Code:

xtemp = [];
sdpvar m
for i=1:length(x)
xtemp = [xtemp;x(i)^m];
end
x = xtemp
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