Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities

By Daoli Zhu, Patrice Marcotte. 1996

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In Mathematical Optimization

Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, background): “…the condition of expected co-coercivity, we ﬁrst review some details on co-coercivity, an intermediate notion between monotonicity and strong monotonicity [Zhu and Marcotte, 1996], and explain where it belongs as assumption in the literature of variational inequalities and min-max optimization.”
Communication trade-offs for synchronized distributed SGD with large step size (2019, background): “Almost sure L-co-coercivity (Zhu and Marcotte, 1996) is for example satisfied if for any (p, k) ∈ [P ]× [N t], there exist a random function f t p,k such that gt p,k = (f t p,k) and which is a.”
A Singular Value Thresholding Algorithm for Matrix Completion (2008, background): “The convergence of projected gradient-descent algorithms has been well studied, see [6, 25, 38, 43, 45, 52, 68] for example.”
Stochastic Variance Reduction Methods for Saddle-Point Problems (2016, background): “However, this is a situation where the operators Bi have an extra property called co-coercivity [6], 7”
A splitting algorithm for dual monotone inclusions involving cocoercive operators (2011, background): “In such formulations, cocoercivity often plays a central role; see for instance [2, 6, 11, 13, 19, 20, 21, 23, 28, 29, 30].”
Dynamical systems and forward–backward algorithms associated with the sum of a convex subdifferential and a monotone cocoercive operator (2014, background): “The abstract formulation (1) covers a large variety of problems in physical and decision sciences, see for example [4], [9], [19], [53], and the discussion at the end of the paper.”
On iterative methods for equilibrium problems (2009, methodology): “methods, physical and mathematical formulation of problems 91) and (2); see [1-20].”
Some developments in general variational inequalities (2004, methodology): “It can be shown [13,25,80,87,98,99,150] that various classes of methods including projection, Wiener–Hopf, decomposition and descent can be obtained from this technique as special cases.”
Iterative Schemes for Solving Mixed Variational-Like Inequalities (2001, background): “Condition (13) and inequality (15) show that the sequence {Λ(xn )} is strictly decreasing (unless xnGx*) and is nonnegative by (7).”
Variable metric forward–backward splitting with applications to monotone inclusions in duality (2012, background): “This framework is quite central due to the large class of problems it encompasses in areas such as partial differential equations, mechanics, evolution inclusions, signal and image processing, best approximation, convex optimization, learning theory, inverse problems, statistics, game theory, and va”
Bridging the gap between constant step size stochastic gradient descent and Markov chains (2017, background): “Almost sure L-co-coercivity [59] is for example satisfied if for any k ∈ N∗, there exists a random function fk such that f ′ k = (fk) ′ and which is a.s. convex and L-smooth.”
Invex equilibrium problems (2005, methodology): “5 are exactly the iterative methods for solving convex equilibrium problems and variational inequalities, see [19,40,41].”