optimization of multivariate portfolio.

Hi everyone,

I want to construct the weights of a multivariate portfolio that includes 6 assets. However, I need to constraint the sum of the weights for every time t to be between -1 and 2.

The actual problem is that the investor wants to maximize r=w'a+(1-w'1)i for every time t. subject to the constraints: s^2=w'VCVw , where s is the target conditional volatility for the portfolio returns, w are the weights of the multivariate portfolio, say 6x1, VCV is the variance-covariance matrix for every time t Σx_i>=-1 for every t Σx_i<=2 for every t.

Any help is appreciated. Thanks in advance