A class of gap functions for variational inequalities

By Torbjörn Larsson, Michael Patriksson. 1994

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In Mathematical Optimization

Citations in the corpus

Frank-Wolfe Algorithms for Saddle Point Problems (2016, background): “By convex-concavity, h t can be upper-bounded by the following FW linearization gap (Jaggi, 2011, 2013; Larsson and Patriksson, 1994; Zhu and Marcotte, 1998): t .”
A Variational Inequality Perspective on Generative Adversarial Networks (2018, background): “More formally, a function g : Larsson and Patriksson, 1994).”
Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets (1998, background): “an (approximate) line search with respect to a merit function for (5.1); see [ 37 , 54, 57] for more details.”
Convergence Properties of Feasible Descent Methods for Solving Variational Inequalities in Banach Spaces (1998, background): “Convergence results for descent algorithms have been obtained under the weaker assumption that the mapping be monotone (see Zhu and Marcotte [19] and Patriksson [14]).”
A Variational Inequality Perspective on Generative Adversarial Nets (2018, background): “More formally, a function g : X → R is called a merit function if g is a non-negative function such that g(x) = 0 ⇔ x ∈ X ∗ (Larsson and Patriksson, 1994).”
Some developments in general variational inequalities (2004, background): “It has been shown that this theory provides the most natural, direct, simple, unified and efficient framework for a general treatment of a wide class of unrelated linear and nonlinear problems, see, for example, [1–150] and the references therein.”