[R] maximization help :

[mingan yang]

 Given a vector  : pvec=(p1,p2,.... p J)   with sum(pvec)=1,   all the 
elements are non-negative, that is, they are probabilities

 a  matrix   A  ( N* J ), with the elements  alpha(ij)  are 0 or 1


    I want to MAXIMIZE THE RESULT

      RESULT=   product( i=1, to N   [ sum (  alpha(ij)* pj , j =1,to J 
) ]  )

    thus, I need to get pvec. how should I do ?
 
      for example 

            
    say, A=  0   1   0   0
                 1    1  0   0
                 1   0   0   0
                0   0   1   0
                1  0    0   1
               0   0    0   1

   that is A is a matrix 6* 4    thus pvec=(p1,p2,p3,p4)

    I want to get  values of pvec such that , they can maximize

   p2 *  ( p1 + p2 ) * p1 * p3 * (p1+p4) * p4

 
  thanks