List of constraints in Minimize

I’m seeking a technique to automate a list of constraints in Mathematica. A sample piece of code is given below; it’s designed to take a 3D cube [0, 1]^3, sample 5 points uniformly randomly from this cube, scale + translate them to [-1, 1]^3, and use them in 5 constraints in the optimization problem "Minimize". I’ve hardcoded the constraints for the moment:

dimuncertset = 3; numsamples = 5; sampinposcube =    RandomVariate[UniformDistribution[dimuncertset], numsamples]; sampincube =    2*sampinposcube + ConstantArray[-1, {numsamples, dimuncertset}]; res = FindMinimum[{t,     t >= x Norm[sampincube[[1]], Infinity] -        Norm[sampincube[[1]], Infinity]^2 &&      t >= x Norm[sampincube[[2]], Infinity] -        Norm[sampincube[[2]], Infinity]^2 &&       t >= x Norm[sampincube[[3]], Infinity] -        Norm[sampincube[[3]], Infinity]^2 &&      t >= x Norm[sampincube[[4]], Infinity] -        Norm[sampincube[[4]], Infinity]^2 &&      t >= x Norm[sampincube[[5]], Infinity] -        Norm[sampincube[[5]], Infinity]^2, - 10 <= t <= 10,     0 <= x <= 1}, {t, x}] 

Any pointer will be appreciated.