  At each iteration of a Block Coordinate Descent method one minimizes an
approximation of the objective function with respect to a generally small set
of variables subject to constraints in which these variables are involved. The
unconstrained case and the case in which the constraints are simple were
analyzed in the recent literature. In this paper we address the problem in
which block constraints are not simple and, moreover, the case in which they
are not defined by global sets of equations and inequations. A general
algorithm that minimizes quadratic models with quadratric regularization over
blocks of variables is defined and convergence and complexity are proved. In
particular, given tolerances $\delta>0$ and $\varepsilon>0$ for
feasibility/complementarity and optimality, respectively, it is shown that a
measure of $(\delta,0)$-criticality tends to zero; and the the number of
iterations and functional evaluations required to achieve
$(\delta,\varepsilon)$-criticality is $O(\varepsilon^2)$. Numerical experiments
in which the proposed method is used to solve a continuous version of the
traveling salesman problem are presented.
