Convergence of proximal solutions for evolution inclusions with time-dependent maximal monotone operators

Abstract This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in optimization algorithms and modeling physical systems. The inclusion described a set-valued mapping having property that, for given time instant, describes maximal monotone operator. By successive application proximal operator, we construct sequence functions parameterized sampling that corresponds to discretization continuous-time system. Under certain mild assumptions on regularity with respect argument, using appropriate tools from functional variational analysis, this then shown converge unique solution original inclusion. result applied develop conditions well-posedness equations interconnected nonsmooth complementarity relations, passivity underlying dynamics (equivalently expressed terms linear matrix inequalities).