Old question but since I'm facing the same problem I thought to post my 2p...
Use quadratic programming as suggested by @Elvis but using sqlincon from the pracma package. I think the advantage over
quadrpog::solve.QP is a simpler user interface to specify the constraints. (In fact,
lsqlincon is a wrapper around
# Test data
X <- matrix(runif(300), ncol=3)
Y <- X %*% c(0.2, 0.3, 0.5) + rnorm(100, sd=0.2)
# Equality constraint: We want the sum of the coefficients to be 1.
# I.e. Aeq x == beq
Aeq <- matrix(rep(1, ncol(X)), nrow= 1)
beq <- c(1)
# Lower and upper bounds of the parameters, i.e [0, 1]
lb <- rep(0, ncol(X))
ub <- rep(1, ncol(X))
# And solve:
lsqlincon(X, Y, Aeq= Aeq, beq= beq, lb= lb, ub= ub)
 0.1583139 0.3304708 0.5112153
Same results as Elvis's:
Rinv <- solve(chol(t(X) %*% X));
C <- cbind(rep(1,3), diag(3))
b <- c(1,rep(0,3))
d <- t(Y) %*% X
solve.QP(Dmat = Rinv, factorized = TRUE, dvec = d, Amat = C, bvec = b, meq = 1)$solution
EDIT To try to address gung's comment here's some explanation. sqlincon emulates matlab's lsqlin which has a nice help page. Here's the relevant bits with some (minor) edits of mine:
X Multiplier matrix, specified as a matrix of doubles. C represents the multiplier of the solution x in the expression C*x - Y. C is M-by-N, where M is the number of equations, and N is the number of elements of x.
Y Constant vector, specified as a vector of doubles. Y represents the additive constant term in the expression C*x - Y. Y is M-by-1, where M is the number of equations.
Aeq: Linear equality constraint matrix, specified as a matrix of doubles. Aeq represents the linear coefficients in the constraints Aeq*x = beq. Aeq has size Meq-by-N, where Meq is the number of constraints and N is the number of elements of x
beq Linear equality constraint vector, specified as a vector of doubles. beq represents the constant vector in the constraints Aeq*x = beq. beq has length Meq, where Aeq is Meq-by-N.
lb Lower bounds, specified as a vector of doubles. lb represents the lower bounds elementwise in lb ≤ x ≤ ub.
ub Upper bounds, specified as a vector of doubles. ub represents the upper bounds elementwise in lb ≤ x ≤ ub.