# Question:second order cone optimization

## Question:second order cone optimization

Maple

My next project will be to understand second order cone optimization
and submit an easy to understand example to the maple application
center inorder to help other people understand it as well. Due to the
extreme technical nature of the problem I have offered various "experts"
up to 500 USD if they can explain it to me in simple terms.

Most optimization people have told me: We want \$\$\$\$\$\$\$\$ to explain it to you.
Apparently, everyone ells should share their knowledge to the world
except for these guys. This has just increased my willingness to expose
the solution.

I was wondering if anyone has some basic understanding of what such
optimization algorithm will look like in Maple? Preferably a finance example.
I have below summarized some information I have found about the problem at hand:

1) every linear programming problem is a conic optimization problem

2) Cone optimization can quickly and reliably solve large size problems.

3) Convex quadratic programming (QP) such as portfolio construction
and risk budgeting problems can be formulated as conic optimization problems.

4) A quadratic objective xTQx can be handled by introducing a new variable t,
making the objective "minimize t", adding the constraint  xTQx <= t,
and converting this constraint to SOC form

5) Since an SOC constraint is a second order function, its Hessian
(the matrix of its second partial derivatives with respect to the decision variables)
is constant.

6) Once the Hessians are obtained, an Interior Point method can solve an
SOCP problem in roughly the same time as an LP problem of equivalent size.
And since SOCP problems are always convex, we can be assured of finding
the globally optimal solution.

http://www.solver.com/probconic.htm

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