Finite-Dimensional Variational Inequalities and Complementarity Problems

By Francisco Facchinei, Jong-Shi Pang. 2003

5,830 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis, Mathematical Optimization

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Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, background): “What we can show instead is that a L-Lipschitz and μ-strongly monotone operator is `–co-coercive with ` ∈ [L,L(2)/μ] [Facchinei and Pang, 2007].”
A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, methodology): “Through a similar spectral approach, Gidel et al. (2019b) study the dynamics of the gradient method with or without momentum and advocate the use of negative momentum and alternating updates based on the analysis of bilinear examples.”
Reducing Noise in GAN Training with Variance Reduced Extragradient (2019, background): “(8) Note that for a L-Lipschitz and µ-strongly monotone operator, we have ` 2 [L,L2/µ] (Facchinei and Pang, 2003).”
Convex Optimization in Signal Processing and Communications (2009, methodology): “For this purpose, we need the framework given by the more advanced theory of finite-dimensional VIs [32, 67] that provides a satisfactory resolution to the game GVI, as detailed next.”
Explicit iterative algorithms for solving equilibrium problems (2019, background): “This section presents some fundamental experiments on amodel which generalizes the Nash-Cournot oligopolistic equilibriummodel [10].”
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems (2009, neutral): “In the optimization literature, this algorithm can be traced back to the proximal forwardbackward iterative scheme introduced in [6 ]a nd [30] within the general framework of splitting methods; see [ 14, Chapter 12 ] and the references therein for a very good introduction to this approach, including”
On the co-derivative of normal cone mappings to inequality systems ☆ (2009, background): “Summarizing, CQ∗ is something in between LICQ and MFCQ and it seems that it is closely related to the constant rank constraint qualification CRCQ (see [11]).”
Outer approximation methods for solving variational inequalities in Hilbert space (2017, background): “In the last decades, VIs have been extensively studied by many authors; see, for example, Facchinei’s and Pang’s two-volume book [1], the review papers by Xiu and Zhang [2], and Noor [3], as well as a recent one by Chugh and Rani [4].”
Using EPECs to Model Bilevel Games in Restructured Electricity Markets with Locational Prices (2007, background): “, Facchinei and Pang (2003). What may be novel is to approach stationarity of bilevel programs, hence bilevel games, via MPECs.”
Hybrid Variance-Reduced SGD Algorithms For Minimax Problems with Nonconvex-Linear Function (2020, background): “, in game theory, robust optimization, distributionally robust optimization, and generative adversarial nets (GANs) [4, 10, 12, 30].”