Double Summation expression in Objective Function

Hi Experts, I have a Parameter matrix, C of size 2x2. It looks like this.

C= [2 4; 6 8]

I have a decision variable, X of size 2x2. It looks like this

   [ X('S1', 'D1')    X('S1', 'D2')    ]
   [ X('S2', 'D1')    X('S2', 'D2')   ]

I want to formulate my Objective Function as a series of double expression (Please refer the attachment),

Which shall look like the following after the expansion.

Z = 2*X('S1', 'D1')  + 4*X('S1', 'D2') + 6*X('S2', 'D1')  + 8*X('S2', 'D2')

I try the following.

Z = sum(C.*X,1);

But it creates An optimizationExpression of size 1x3, which is not desired.

What am I doing wrong? Is there any easier way to do so without using for loop. I have just started learning "Problem-Based Optimization" in MATLAB today. Any help will be greatly appreciated.

Answer 1

[Mary Fenelon]

Was it a 1x3 OptimizationExpression or 1x2?

In any case, you need to sum over both dimensions to get a single OptimizationExpression

    Z = sum(sum(C.*X))

[pradeep kumar]

@ Mary Fenelon, Thanks for your solution. It should be actually 1x2 OptimizationExpression, Sorry for my typing mistake. Could you please explain me the logic behind this? I have triple summation and more expressions in the future prob lem.Thanks in advance!

[Mary Fenelon]

Look here for documentation on the sum function. This example has a 3 dimensional OptimizationVariable.