[OS] linear constraint terms in OSInstace API

[Kipp Martin]

Hi Susana:

> 
> I am using OSInstace API to represent my nonlinear problem. 
> What is exactly the meaning of <start> when defining the linear constraint terms in c++ ?


We built the OSInstance API to efficiently represent the constraint 
matrix of linear programs, or the linear part of a nonlinear program. 
Let's say I have two constraints:

x0 + 10.5x02 + 11.7x12 + 3*x0*x1 <= 25
ln(x0*x1) + 7.5x0 + 5.25x1 >= 10

I have three linear terms in these two constraints. I would represent 
the three linear terms by

     <start>
         <el>0</el><el>2</el><el>3</el>
     </start>
     <rowIdx>
         <el>0</el><el>1</el><el>1</el>
     </rowIdx>
     <value>
         <el>1.</el><el>7.5</el><el>5.25</el>
     </value>

In this case we are storing the linear terms by columns (hence the 
<rowIdx>). The <start> indicates the start of the nonzero elements. So 
variable x0 starts at position 0. It has two coefficients 1 and 7.5. 
Then variable x1 starts in position 2 and has one term 5.25. The number 
of starts is number of variables + 1. The last start value of 3 
indicates that there are 3 nonzeros that we are storing.

Regards


> 
> 
> Thanks. 
> 
> 
> Regards, 
> Susana Lera.
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-- 
Kipp Martin
Professor of Operations Research
and Computing Technology
Graduate School of Business
University of Chicago
5807 South Woodlawn Avenue
Chicago, IL 60637
773-702-7456
kipp.martin at chicagogsb.edu
http://gsbkip.chicagogsb.edu
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