This question is a follow-up question on my earlier one regarding LSq optimization in Excel.
Essentially, I have set up the following LSq in excel (thanks again to fmarshal for his insightful help on this)
- Given is a vector of original exposure across a range of seven nodes (B8:H9)
- The aim is to replicate this exposure at each point as close as possible from a set of 5 instruments. The contribution of each instrument on any of the 7 nodes is represented in the matrix B11:HI15
- I then solve for the number of units of each instrument (I11:I15) such that the sum of the squared differences (cell C24) is minimized , using solver (GRG Nonlinear, using constraints of =<1,000,000,000 & > -1,000,000,0000 for the decision variable cells)
Now this is essentially a set-up that assigns equal weightings (importance) to each node.
I now would like to assign relative weightings to the respective nodes, with the aim that the optimization assigns greater importance to find a good fit to say one specific node relative to others (in effect create sort of a 'hierarchy' among the nodes)
In the attached spreadsheet, I have added such exemplary node-weights in row 9; however, I don't quite know where/how to integrate them into the optimization. Any feedback would be most appreciated.