Problem formulation

I want to solve the following problem in CVX.

min_{t,d} t+.5*d'*d
s. t. a_i*d+g_i(x+d)-g_i(x)<=t 
i=1,2,..,m
lb<=x+d<=ub

t\in R, d\in R^n

where g_i is convex nodifferentiable nonlinear function, a_i are row vector, x is parameter.