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Regression Formulation

Priyan Fernando
Posted 10 years ago

Hi Everyone! I am trying to formulate a regression problem in the form of the following equation (which is from a portfolio optimization example code found here)

Eq. 1 - Portfolio Optimization Equation enter image description here For the regression we have that enter image description here Which simplifies to: enter image description here? Thus this should be the same form as Eq. 1? With the Betas=x, Lambda=1, Q=X'X and r = 2y'X? Since y'y is a scalar it can be ignored?

The reason I ask is because I want to modify some code (http://in.mathworks.com/help/optim/examples/mixed-integer-quadratic-programming-portfolio-optimization.html) so that I can run a regression problem instead, but the code is giving some errors (not converging). I would like help in verifying my approach of reformulating this problem is correct?

Thank you, Priyan.
POSTED BY: Priyan Fernando
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Priyan Fernando
Priyan Fernando
Posted 10 years ago

Hi Otto,

Thank you for your comments. Yes I am indeed trying to run a regression (chose x to minimize ||Ax-b|| ) but with the additional constraint that, for the elements of x: x=0 or lb<= x <= ub. Here lb/up are the lower and upper bounds respectively. If I only had the constraint: lb<= x <= ub then I could solve that using quadratic programming. The complication arises because elements of x could also be 0.

I think solving there is no built in function to solve this in Mathematica? I have however spotted such a feature in Matlab (http://in.mathworks.com/help/optim/examples/mixed-integer-quadratic-programming-portfolio-optimization.html). Do you know of how to solve this in Mathematica? The actual problem is also quite large, e.g. x has 20000 elements, and A is of dimension 20000x500.

Thanks!
POSTED BY: Priyan Fernando
POSTED BY: Otto Linsuain
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