  This paper focuses on finite-time (FT) convergent distributed algorithms for
solving time-varying (TV) distributed optimization (TVDO). The objective is to
minimize the sum of local TV cost functions subject to the possible TV
constraints by the coordination of multiple agents in finite time.
Specifically, two classes of TVDO are investigated included unconstrained
distributed consensus optimization and distributed optimal resource allocation
problems (DORAP) with both TV cost functions and coupled equation constraints.
For the previous one, based on non-smooth analysis, a continuous-time
distributed discontinuous dynamics with FT convergence is proposed based on an
extended zero-gradient-sum method with a local auxiliary subsystem. Then, an FT
convergent distributed dynamics is further obtained for TV-DORAP by dual
transformation. Particularly, the inversion of the cost functions' Hessians is
not required in the dual variables' dynamics, while another local optimization
needs to be solved to obtain the primal variable at each time instant. Finally,
two numerical examples are conducted to verify the proposed algorithms.
