On the Stability of Globally Projected Dynamical Systems

By Youshen Xia, Jun Wang. 2000

212 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/6379a9cb553cbbbd4f8774df0916bd387d85a93b

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In Computational Theory and Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems (2015, methodology): “…analyze the convergence of (9), The analysis techniques are inspired by the projected dynamical systems for variational inequalities (referring to Xia & Wang (2000) and Gao (2003)) and distributed optimization (referring to Shi, Johanssan, & Hong (2013 ), Kia, Cort´es, & Martinez (2015), Qiu,…”
New Trends in General Variational Inequalities (2020, background): “For recent state-of-the-art in this field, see [1-200] and the references therein.”
Distributed Maneuvering of Autonomous Surface Vehicles Based on Neurodynamic Optimization and Fuzzy Approximation (2018, methodology): “In [43], it is shown that the RNN (13) is globally exponentially convergent to the optimal solution of (12).”
Further Results on Global Convergence and Stability of Globally Projected Dynamical Systems (2004, background): “Then, the KKT point is equivalent to the solution of ( 2 ), where � = R n+m and u = [x,y ] T .”
Nash-type equilibria on Riemannian manifolds: a variational approach (2016, background): “Note that the aforementioned results concerning the ’projected’ dynamical system (CDS)α are new even in the Euclidean setting; see Cavazzuti, Pappalardo and Passacantando [8], Xia [35], and Xia and Wang [36].”
Output-Feedback Path-Following Control of Autonomous Underwater Vehicles Based on an Extended State Observer and Projection Neural Networks (2018, methodology): “In the literature, many efficient and effective neurodynamic optimization methods are proposed for solving optimization problems [52], [67], [68].”
Some developments in general variational inequalities (2004, methodology): “gðunþ1Þ ¼ PK ½gðunÞ anTg 1ðgðunÞ gnRðunÞÞ ; n ¼ 0; 1; 2; . . . ; ð3:13Þ where an ¼ ðgn rÞkRðunÞk 2 kTg 1ðgðunÞ gnRðunÞÞk 2 : ð3:14Þ For g I , where I is the identity operator, we obtain a variant form of the modified extragradient-type methods for solving variational inequalities, which have been st”