[GSoC-PortA] Question on quadratic constraint specification

[Ross Bennett]

Hi All,

I have a quick question on quadratic constraint specification. One of the
bullet points under constraints is "provide quadratic constraint
specification". I did some digging for the ROI solvers and found that
quadprog and glpk only handle linear constraints. The ROI plugin for cplex
can handle a quadratic constraint, but this is a commercial product so I am
not sure if we want to go down that road and add support for the cplex
plugin for optimize_method="ROI". Are there workarounds to handle quadratic
constraints in quadprog or glpk?

Is the intent of providing quadratic constraint specification to allow the
user to specify or define any function?

Or should we limit it to pre-defined constraint types and functions that I
can add?

A couple use cases for a quadratic constraint that I thought of are:
- Diversification (Allows the user to specify a diversification limit as a
constraint).
- Volatility (Allows the user to specify a target volatility (or min or
max) as a constraint. (e.g. see Peter Carl's email with a portfolio
specific limit to target volatility of > 10%)
- Other use cases for quadratic constraints?

I can add constraint functions for diversification, volatility, etc. and
then this could be implemented in constrained_objective or with the mapping
function that I will work on in the next section.

Thanks,
Ross Bennett
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