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(This article was first published on <strong><a href="http://zoonek.free.fr/blosxom/2012/06/01#2012-06-01_Optimization"> Vincent Zoonekynd's Blog </a></strong>, and kindly contributed to <a rel="nofollow" href="https://www.r-bloggers.com/">R-bloggers)</a> </div>
<p>Many problems in statistics or machine learning<br>
are of the form “find the values of the parameters<br>
that minimize some measure of error”.<br>
But in some cases, constraints are also imposed<br>
on the parameters: for instance, that they should sum up to 1,<br>
or that at most 10 of them should be non-zero —<br>
this adds a combinatorial layer to the problem,<br>
which makes it much harder to solve.
</p>
<p>In this note,<br>
I will give a guide to (some of) the optimization packages in R<br>
and explain (some of) the algorithms behind them.<br>
The solvers accessible from R have some limitations,<br>
such as the inability to deal with binary or integral constraints<br>
(in non-linear problems): we will see how to solve such problems.
</p>
<p>When you start to use optimization software,<br>
you struggle to coax the problem into the form expected<br>
by the software (you often have to reformulate it to make it<br>
linear or quadratic, and then write it in matrix form).<br>
This is not very user-friendly.<br>
We will see that it is possible to specify optimization problems<br>
in a perfectly readable way.
</p>
<pre># Actual R code
x &lt;- variable(5)
minimize( sum(abs(x)) + sum(x^2) - .2*x[1]*x[2] )
x >= 0
x &lt;= 1
sum(x) == 1
x[1] == x[2] 
r &lt;- solve()</pre>
<p>Many of the examples will be taken from finance and portfolio optimization.
</p>
<p><img alt="2012-06-01_Biased_Random_Portfolios.png" src="https://i2.wp.com/zoonek.free.fr/blosxom//R/2012-06-01_Biased_Random_Portfolios.png?w=456" data-recalc-dims="1"></p>
<p>&lt;p>&lt;a href=”http://zoonek.free.fr/blosxom/R/2012-06-01_Optimization.html?seemore=y” class=”seemore”>See more …&lt;/a>&lt;/p></p>
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<div>To <strong>leave a comment</strong> for the author, please follow the link and comment on their blog: <strong><a href="http://zoonek.free.fr/blosxom/2012/06/01#2012-06-01_Optimization"> Vincent Zoonekynd's Blog </a></strong>.</div>
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