https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 Metric regularity and Lipschitzian stability of parametric variational systems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11705 Wed 11 Apr 2018 15:39:28 AEST ]]> Uniformity and inexact version of a proximal method for metrically regular mappings https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11704 Wed 11 Apr 2018 14:26:49 AEST ]]> Enhanced metric regularity and Lipschitzian properties of variational systems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11706 Wed 11 Apr 2018 14:09:13 AEST ]]> Metric regularity of Newton’s iteration https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11707 Wed 11 Apr 2018 13:33:45 AEST ]]> A new and self-contained proof of Borwein’s norm duality theorem https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11703 Wed 11 Apr 2018 13:04:20 AEST ]]> Global convergence of a non-convex Douglas-Rachford iteration https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13497 Wed 11 Apr 2018 11:19:02 AEST ]]> On the inner and outer norms of sublinear mappings https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11702 Wed 11 Apr 2018 09:22:48 AEST ]]> Walking on real numbers https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:12958 Sat 24 Mar 2018 10:37:17 AEDT ]]> A Lyusternik-Graves theorem for the proximal point method https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11708 Sat 24 Mar 2018 10:32:01 AEDT ]]> Convergence of the proximal point method for metrically regular mappings https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:11701 n : X → Y with gn(0) = 0 that are Lipschitz continuous in a neighborhood of the origin. Then pick an initial guess x0 and find a sequence xn by applying the iteration gn(xn1-xn)+T(xn+1) ∋ 0 for n = 0,1,... We prove that if the Lipschitz constants of gn are bounded by half the reciprocal of the modulus of regularity of T, then there exists a neighborhood O of x̅ (x̅ being a solution to T(x) ∋ 0) such that for each initial point x₀ ∈ O one can find a sequence xn generated by the algorithm which is linearly convergent to x̅. Moreover, if the functions gn have their Lipschitz constants convergent to zero, then there exists a sequence starting from x₀ ∈ O which is superlinearly convergent to x̅. Similar convergence results are obtained for the cases when the mapping T is strongly subregular and strongly regular.]]> Sat 24 Mar 2018 10:32:00 AEDT ]]> Applications of convex analysis within mathematics https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:19192 Sat 24 Mar 2018 07:55:02 AEDT ]]> Recent results on Douglas-Rachford methods for combinatorial optimization problems https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:28771 Sat 24 Mar 2018 07:23:45 AEDT ]]>