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Metric subregularity of the convex subdifferential in Banach spaces Aragón Artacho, Francisco Javier ; in Journal of Nonlinear and Convex Analysis (2014), 15(1), 35-47 In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated ... [more ▼] In [2] we characterized in terms of a quadratic growth condition various metric regularity properties of the subdifferential of a lower semicontinuous convex function acting in a Hilbert space. Motivated by some recent results in [16] where the authors extend to Banach spaces the characterization of the strong regularity, we extend as well the characterizations for the metric subregularity and the strong subregularity given in [2] to Banach spaces. We also notice that at least one implication in these characterizations remains valid for the limiting subdifferential without assuming convexity of the function in Asplund spaces. Additionally, we show some direct implications of the characterizations for the convergence of the proximal point algorithm, and we provide some characterizations of the metric subregularity and calmness properties of solution maps to parametric generalized equations [less ▲] Detailed reference viewed: 33 (7 UL)Characterization of metric regularity of subdifferentials Aragón Artacho, Francisco Javier ; in Journal of Convex Analysis (2008), 15(2), 365-380 We study regularity properties of the subdifferential of proper lower semicontinuous convex functions in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the strong ... [more ▼] We study regularity properties of the subdifferential of proper lower semicontinuous convex functions in Hilbert spaces. More precisely, we investigate the metric regularity and subregularity, the strong regularity and subregularity of such a subdifferential. We characterize each of these properties in terms of a growth condition involving the function. [less ▲] Detailed reference viewed: 95 (6 UL)Uniformity and inexact version of a proximal method for metrically regular mappings Aragón Artacho, Francisco Javier ; in Journal of Mathematical Analysis & Applications (2007), 335(1), 168-183 We study stability properties of a proximal point algorithm for solving the inclusion 0∈T(x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of ... [more ▼] We study stability properties of a proximal point algorithm for solving the inclusion 0∈T(x) when T is a set-valued mapping that is not necessarily monotone. More precisely we show that the convergence of our algorithm is uniform, in the sense that it is stable under small perturbations whenever the set-valued mapping T is metrically regular at a given solution. We present also an inexact proximal point method for strongly metrically subregular mappings and show that it is super-linearly convergent to a solution to the inclusion 0∈T(x). [less ▲] Detailed reference viewed: 45 (4 UL) |
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