  A first characterization of many exoplanets has recently been achieved by the
observational determination of their radius. For some planets, a measurement of
the luminosity has also been possible, with many more directly imaged planets
expected in the future. The statistical characterization of exoplanets through
their mass-radius and mass-luminosity diagram is thus becoming possible. This
is for planet formation and evolution theory of similar importance as the
mass-distance diagram. Our aim in this and a companion paper is to extend our
formation model into a coupled formation and evolution model. We want to
calculate in a self-consistent way all basic characteristics (M,a,R,L) of a
planet and use the model for population synthesis calculations. Here we show
how we solve the structure equations describing the gaseous envelope not only
during the early formation phase, but also during gas runaway accretion, and
during the evolutionary phase at constant mass on Gyr timescales. We then study
the in situ formation and evolution of Jupiter, the mass-radius relationship of
giants, the influence of the core mass on the radius and the luminosity both in
the "hot start" and the "cold start" scenario. We put special emphasis on the
comparison with other models. We find that our results agree very well with
those of more complex models, despite a number of simplifications. The upgraded
model yields the most important characteristics of a planet from its beginning
as a seed embryo to a Gyr old planet. This is the case for all planets in a
synthetic planetary population. Therefore, we can now use self-consistently the
statistical constraints coming from all major observational techniques. This is
important in a time where different techniques yield constraints on very
diverse sub-populations of planets, and where its is challenging to put all
these constraints together in one coherent picture.
