… that w is a second-order stationary point of F(w) and output w. … Guarantees In this section,
we provide the theoretical result guaranteeing that Algorithm 1 converges to a second-order …

… second-order distributed dynamics was proposed to solve an unconstrained optimization in
[11], while a similar algorithm … the connectivity of graph G , which guarantees that any agent’s …

… makes distributed computation of primal gradients impossible. … pendency of the convergence
constant with the algorithm’s … To guarantee that the second order approximation suggested …

… While some firstorder algorithms can guarantee … comparisons among first and secondorder
methods, we consider … which involve comparisons among various second-order methods, we …

… guarantees on the sampling error of these second-order LMCs. These guarantees reveal that
the second-order LMC algorithms … providing guarantees for sampling from a distribution in …

… the second-order terms of a cost function to overcome the disadvantages of gradient (multiplicative)
algorithms. … The convergence of the CG is guaranteed in a finite number of iterations …

… network only impacts a second-order term in O(1/t), where t is … yet efficient algorithm called
distributed randomized smoothing … Our performance guarantee for the MSPD algorithm is then …

… powerful local solver, such as a second order method), so that … differences, which we
call DIANA (Algorithm 1). Unlike the … , number of iterations sufficient to guarantee that E∥∇f(xk)∥2 …

… : assuming independently and identically distributed (iid) gaussian … and does not guarantee
positive definiteness. Practical … of common secondorder gradient algorithms, including the …

… Under an appropriate initial condition, it is shown that the second-order distributed algorithms
guarantees to find an optimal solution and also has the advantage of keeping the power …