==========
Optimizers
==========

.. contents::

Comparison of `aopt` and `nopt`
===============================

If your portfolio optimization problem can be expressed as a combination of
linear equality constraints and soft equality constraints, then use
``aopt``. The analytical optimizers is much faster and is guaranteed
(by math, not by meva) to give the optimal portfolio.

If, however, you need to specify separately the sum of the short and long
positions in your portfolio or have some other constraints that ``aopt``
does not handle, then use ``nopt``.

======================   ==================  ==================
attribute                aopt                nopt
======================   ==================  ==================
fast                     :math:`\checkmark`     
guaranteed optimal       :math:`\checkmark`     
linear constraints       :math:`\checkmark`     
soft constraints         :math:`\checkmark`  :math:`\checkmark`
sum longs, shorts                            :math:`\checkmark`
position limits                              :math:`\checkmark`
turnover limit                               :math:`\checkmark`
inequality constraint                        :math:`\checkmark`
transaction cost                             :math:`\checkmark`
======================   ==================  ==================

The meva benchmark suite::

    >>> meva.bench(nasset=300, nfactor=4, nrepeat=5)
    Meva performance benchmark
        Meva 0.0.2dev
        Mean wall clock time in seconds
        nassets=300, nfactor=4, nrepeat=5

      aopt     nopt
      0.0023   0.7002    sum 1
               0.8057    longs sum 1, shorts -1
               0.8027    longs sum 1, shorts -1; linear transaction costs
               0.0551    longs sum 1, shorts -1; position limit +- 2/nasset
               0.1255    longs sum 1, shorts -1; position limit +- 4/nasset 

Examples
========