  A variational model is proposed to describe the magnetic properties of
type-II superconductors in the entire field range between $H_{c1}$ and $H_{c2}$
for any values of the Ginzburg-Landau parameter $\kappa>1/\sqrt{2}$. The
hexagonal unit cell of the triangular flux-line lattice is replaced by a circle
of the same area, and the periodic solutions to the Ginzburg-Landau equations
within this cell are approximated by rotationally symmetric solutions. The
Ginzburg-Landau equations are solved by a trial function for the order
parameter. The calculated spatial distributions of the order parameter and the
magnetic field are compared with the corresponding distributions obtained by
numerical solution of the Ginzburg-Landau equations. The comparison reveals
good agreement with an accuracy of a few percent for all $\kappa$ values
exceeding $\kappa \approx 1$. The model can be extended to anisotropic
superconductors when the vortices are directed along one of the principal axes.
The reversible magnetization curve is calculated and an analytical formula for
the magnetization is proposed. At low fields, the theory reduces to the London
approach at $\kappa \gg 1$, provided that the exact value of $H_{c1}$ is used.
At high fields, our model reproduces the main features of the well-known
Abrikosov theory. The magnetic field dependences of the reversible
magnetization found numerically and by our variational method practically
coincide. The model also refines the limits of some approximations which have
been widely used. The calculated magnetization curves are in a good agreement
with experimental data on high-T$_c$ superconductors.
