Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications

By Patrick T. Harker, Jong-Shi Pang. 1990

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In Optimization & Training

Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, methodology): “Also, we do not use the full power of variational inequalities that usually have constraints [Harker and Pang, 1990], but standard algorithms for (1) are coming from this literature [Gidel et al.”
Reducing Noise in GAN Training with Variance Reduced Extragradient (2019, methodology): “In the context of a zero-sum game, for any convex-concave function L and any closed convex sets ⇥ and , the extragradient method converges (Harker and Pang, 1990, Thm. 12.1.11).”
A Variational Inequality Perspective on Generative Adversarial Networks (2018, background): “…can be understood as a two-player game, in the sense of game theory (Von Neumann and Morgenstern, 1944), and can be addressed as a variational inequality problem (VIP) (Harker and Pang, 1990), a framework that encompasses traditional saddle point optimization algorithms (Korpelevich, 1976).”
Stochastic Variance Reduction Methods for Saddle-Point Problems (2016, neutral): “– Variational inequality problems , which are notably common in game theory (see, e.g., [5]).”
Convex Analysis And Nonlinear Optimization (2000, unknown): “A survey of variational inequalities and complementarity problems may be found in [93].”
Coercivity Conditions for Equilibrium Problems (2005, background): “(i) f( · ,y) is upper sign continuous, for every y ∈ K; (ii) lev≤0 f( x,·) is closed, for every x ∈ K; (iii) f (x,y) = 0 ,f (x, z) 1 ); (iv) f( x,·) is quasiconvex, for every x ∈ K; (v) f (x,x) ≥ 0, for every x ∈ K.”
Linear Lower Bounds and Conditioning of Differentiable Games (2019, background): “Game formulations arise commonly in many ﬁelds, such as game theory (Harker and Pang, 1990), machine learning (Kim and Boyd, 2008; Goodfellow et al., 2014), and computer vision (Chambolle and Pock, 2011; Wang et al., 2014) among others, and encompass saddle-point problems (Palaniappan and Bach,…”
Bayesian Nash equilibrium and variational inequalities (2016, background): “…variational inequality problem is a general problem formulation that encompasses a plethora of mathematical problems including nonlinear equations, optimization problems, complementarity problems, and fixed point problems, among others (Harker and Pang, 1990; Ferris and Pang, 1997; Nagurney, 1993).”
Decomposition Methods for Differentiable Optimization Problems over Cartesian Product Sets (1998, background): “, a Nash equilibrium game) [31], commodities of goods in a market or spatial price equilibrium problem [48], or pairs of origins and destinations in a transportation network [56].”