  The purpose of this work is to study an optimal control problem for a
semilinear elliptic partial differential equation with a linear combination of
Dirac measures as a forcing term; the control variable corresponds to the
amplitude of such singular sources. We analyze the existence of optimal
solutions and derive first and, necessary and sufficient, second order
optimality conditions. We develop a solution technique that discretizes the
state and adjoint equations with continuous piecewise linear finite elements;
the control variable is already discrete. We analyze the convergence properties
of discretizations and obtain, in two dimensions, an a priori error estimate
for the underlying approximation of an optimal control variable.
