Question: How to write matrix inequalities (restriction for optimization)

Hi e-friends,

I want to minimize a function subject to a set of S restrictions.

The restrictions are related to matrices V, W, X and Y:

V = [v1, .., vS]  order L x S

W = [w1, .., wS] order L x S

X = [x1, .., xS]  order LxS

Y = [y11,.. yS] order L x S

How may I write in MAPLE in compact form  the following S inequalities (for any arbitrary integers L and S)?. (In my problem L and S can take large values, and I would not like to be writing one by one using the keyboard)

v1.w1        <=    x1.y1

v2.w2         <=   x2.y2

..

vS.wS         <=    xS.yS

(v1.w1 is the inner product of the vectors v1 and w1, each with L elements.

x1. y1 is also the inner product of vector x1 and y1, each with L elements

)

Thanks for you attention,

Jean-Jacques