Optimization problems with the objective function in the form of
weighted sum and linear equality constraints are considered. Given
that the number of local cost functions can be large as well as the
number of constraints, a stochastic optimization method is proposed.
The method belongs to the class of variable sample size first order
methods, where the sample size is adaptive and governed by the addi-
tional sampling technique earlier proposed in unconstrained optimiza-
tion framework. The resulting algorithm may be a mini-batch method,
increasing sample size method, or even deterministic in a sense that
it eventually reaches the full sample size, depending on the problem
and similarity of the local cost functions. Regarding the constraints,
the method uses controlled, but inexact projections on the feasible set,
yielding possibly infeasible iterates. Almost sure convergence is proved
under some standard assumptions for the stochastic framework, with-
out imposing the convexity. Numerical results on relevant problems
from CUTEst collection and real-world data sets for logistic regression
show the stability and the efficiency of the proposed method when
compared to the state-of-the-art methods.