Creation of a lower block triangular matrix of symbolic variables in Yalmip

[Muhammad Yasir]

How can I create a Lower Block  Triangular Matrix of the following form which contains symbolic variables, which are evaluated by solving an optimization problem

where 

;  suppose m = 1, d = 3

values of the entries of this matrix will be evaluated later on through the solution of an optimization problem...

I am trying to solve a Stochastic MPC-based optimization problem...

Is the following code correct to create such a lower block triangular matrix with symbolic variables:

clc

clear all

m = 1;

d= 3;

l_1t = sdpvar(m,d);

l_2t = sdpvar(m,d);

l_2tplus1 = sdpvar(m,d);

l_3t = sdpvar(m,d);

l_3tplus1 = sdpvar(m,d);

l_3tplus2 = sdpvar(m,d);

LAMBDA_t = [zeros(m,d) zeros(m,d) zeros(m,d); l_1t zeros(m,d) zeros(m,d); l_2t l_2tplus1 zeros(m,d); l_3t l_3tplus1 l_3tplus2];

size(LAMBDA_t)

[Johan Löfberg]

LAMBDA_t = tril(sdpvar(N),-1) would be the obvious way to create it from scratch unless I am missing some structure in your notation

[Muhammad Yasir]

tril is a regular command of Matlab to create a lower triangular matrix with a second input argument equal to -1.  While  sdpvar(N) will create an NxN matrix. 

However, the catch here, in this case, is that I want to create a lower block triangular matrix where the dimension of each block matrix is mxd = 1x3

So this regular form of tril command does not seem to work for the creation above mentioned lower block triangular matrix

[Muhammad Yasir]

A similar kind of technique is also discussed on the help page of Yalmip for command 'blkvar'

https://yalmip.github.io/command/blkvar/

[Johan Löfberg]

sound lke you want to combine it with a kron then

>> L = kron(tril(ones(4),-1),ones(2,3));

>> spy(L)

>> L = L.*sdpvar(8,12)

[Muhammad Yasir]

This technique does not seem to work...

[Muhammad Yasir]

I want to implement the following constraint

m = 1;

d = 3;

THETA_t = [zeros(m,d) zeros(m,d) zeros(m,d) zeros(m,d); sdpvar(m,d) zeros(m,d) zeros(m,d) zeros(m,d);... 

    sdpvar(m,d) sdpvar(m,d) zeros(m,d) zeros(m,d); sdpvar(m,d) sdpvar(m,d) sdpvar(m,d) sdpvar(m,d)];

ETA_t = [sdpvar; sdpvar; sdpvar; sdpvar];

constraints1 = [];

constraints1 = [constraints1, abs(ETA_t(i,:))+norm(THETA_t(i,:),1)*phi_max <= Umax];     ---- eq(17)

Since ETA_t and THETA_t involve sdpvar variables. So, is it OK to use implement constraints without using 'implies' statement.

I have read Yalmip help regarding use of 'implies', but I could not understand how to use 'implies' for modeling if-else when sdpvar variables are involved....

I am implemented this paper theoretically but my results are not as expected perhaps, I do not properly understand use of Yalmip

[Johan Löfberg]

I have no idea what you are asking about. All articles about implies and if-else are (of course) involving sdpvars.

[Muhammad Yasir]

OK let me rephrase the question, then would repost my question ... the crux of the matter is I am unable to understand how to use implies for if-else like constraints based on sdpvar variables...

[Johan Löfberg]

https://yalmip.github.io/example/modellingif/