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I have a non linear Sharpe ratio with 3 portfolio weights w1,w2 and w2. I want to (globally) maximize the sharpe ratio by choosing w1,w2 and w2 subject to the constraints that each of the variables is in the range of 0 to 1, and that their summation is equal to 1. I also want the maximization to start at an initial point of [w1=0.35,w2=0.6,w3=0.05].

The function is:

SR:= (0.012w1+0.007w2+0.0384w3-0.009)/(stdev)

where stdev is the standard deviation of the portfolio ...

I'm having trouble maximizing this funciton:

S=  (w1*E1+w2*E2+w3*E3)/(CoVar[1,2]), subject to the constraint w1+w2+w3=1

I need it to choose w1, w2, and w3 to maximize S

Does anybody know how to configure the model to obtain the position constraint equations of a slider-crank mechanism as:

l1·cos(theta)+l2·sin(beta)-s = 0
l1·sin(theta)-l2·cos(beta) = 0

instead as obtained in the help-example on:
http://www.maplesoft.com/support/help/MapleSim/view.aspx?path=MapleSim/Multibody/Kinematic_Exports

Thanks in advance

Ok, when I run the below code which maximize the risk adjuested portfolio returns
(long and short positions) in QP matrix form on empirical data I get very strange
allocations ie we go 100% or 100% short in almost all stocks except for a few
where the allocations are more appropriate like 0.2 etc.


# Maximize Risk Adjuested Return Matrix Form
# Minimize W'.Cov.W−W'.EV
# R=Return Matrix

EV := Vector([seq(ExpectedValue(Column(R, i)), i = 1 .. N)], datatype = float[8]):