Some recent advances in projection-type methods for variational inequalities

By N. Xiu, Jianzhon Zhang. 2003

134 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis, Optimization & Training

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Citations in the corpus

Frank-Wolfe Algorithms for Saddle Point Problems (2016, methodology): “The standard approaches to solve smooth constrained SP problems are projectiontype methods (surveyed in Xiu and Zhang [23]), with in particular variations of Korpelevich’s”
An Efficient Primal-Dual Hybrid Gradient Algorithm For Total Variation Image Restoration (2008, background): “(cid:0) (cid:1) Global convergence is proved for the above algorithm if F is pseudomonotone or Lipschitz continuous or the problem satisfy some local error bound (see [20]), provided the step size α k is small enough to satisfy which can be obtained by simple Armijo type line search.”
New Trends in General Variational Inequalities (2020, background): “For recent state-of-the-art in this field, see [1-200] and the references therein.”
Outer approximation methods for solving variational inequalities in Hilbert space (2017, background): “Examples of such restrictions can be found in the papers by Halpern [16], Lions [17],Wittmann [18], Bauschke [19], Deutsch and Yamada [15], Yamada [21], Xu and Kim [22], Zeng et al. [25], Takahashi and Yamada [26], Aoyama and Kimura [27], and Zhang and He [28].”
New extragradient-type methods for general variational inequalities (2003, methodology): “The extragradient method [1,4,17,29,33,34,36] overcome this difficulty by performing an additional forward step and a projection at each iteration according to the double projection.”
Combined Relaxation Method for Mixed Equilibrium Problems (2005, background): “i.e., (16) is true. Applying ( 8 ) yields � t k ,x k − y k �≥ (ατ � /θ) x k − y k 2 ,”
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.”