Techniques Of Variational Analysis

By Karolin Papst. 2016

301 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

CoCoA: A General Framework for Communication-Efficient Distributed Optimization (2016, background): “The dual relationship in problems (A) and (B) is known as Fenchel-Rockafellar duality (Borwein and Zhu, 2005, Theorem 4.4.2).”
Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization (2020, background): “…using that 1 q k u qp and 1 q ∗ k z q p ∗ are conjugates of each other, which are standard exercises in convex analysis for q ∈ { p, 2 (see, e.g., [9, Exercise 4.4.2] and [10, Example 3.27]). arg } The second part follows by ∇ ψ ∗ ( z ) = sup v R d { z , v − ψ ( v ) , due to Fact 2.3 ( ψ and ψ ∗…”
Error Bounds and Hölder Metric Subregularity (2014, background): “, [5,36] for discussions and characterizations of Asplund spaces.”
METRIC REGULARITY—A SURVEY PART 1. THEORY (2016, background): “By Ekeland’s variational principle (see, for example, [17]) there is a pair (x̂, v̂) ∈ Graph F such that dξ((x̂, v̂), (x, v)) ≤ t and φy(x, v) + rdξ((x, v), (x̂, v̂)) > φy(x̂, v̂) (3.”
Strongly Convex Functions, Moreau Envelopes, and the Generic Nature of Convex Functions with Strong Minimizers (2015, background): “For further information on strong minimizers, we refer readers to [12, 14, 19].”