Block coordinate descent for smooth nonconvex constrained minimization

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