A Panoramic View on Projected Dynamical Systems

Daniele, Patrizia; Giuffrè, Sofia; Maugeri, Andrea; Pia, Stéphane

doi:10.1007/978-1-4419-0158-3_17

Cited by 2 publications

(2 citation statements)

References 31 publications

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“…Projected dynamical systems also appear as special cases in the study of differential inclusions (Aubin and Cellina, 1984) and viability theory (Aubin, 1991). For more recent works that consider projected dynamical systems on manifolds and Banach spaces see Hauswirth et al (2018); Daniele et al (2010) and references therein. In contrast, the independent line of research in Nagurney and Zhang (1996), popular in the context of variational inequalities, uses a different approach which cannot recover the generality of the earlier works.…”

Section: In General [F (X)] Xmentioning

confidence: 99%

Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization

Hauswirth¹,

Ortmann²,

Bolognani³

et al. 2020

Preprint

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In this paper, we study the stability and convergence of continuous-time Lagrangian saddle flows to solutions of a convex constrained optimization problem. Convergence of these flows is well-known when the underlying saddle function is either strictly convex in the primal or strictly concave in the dual variables. In this paper, we show convergence under non-strict convexity when a simple, unilateral augmentation term is added. For this purpose, we establish a novel, non-trivial characterization of the limit set of saddle-flow trajectories that allows us to preclude limit cycles. With our presentation we try to unify several existing problem formulations as a projected dynamical system that allows projection of both the primal and dual variables, thus complementing results available in the recent literature.

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Section: In General [F (X)] Xmentioning

confidence: 99%

Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization

Hauswirth¹,

Ortmann²,

Bolognani³

et al. 2020

Preprint

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show abstract

“…It is also worth mentioning that the solutions to (1) are the critical points of an associated projected dynamical system and, then, there exists a strict connection between evolutionary variational inequalities and projected dynamical systems (see [12][13][14]19,28]). …”

Section: Introductionmentioning

confidence: 99%

Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

Barbagallo

Vincenzo

2011

Journal of Mathematical Analysis and Applications

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We are concerned with an infinite dimensional variational inequality which is connected with the dynamic oligopolistic market equilibrium problem. We will provide existence theorems and show, under minimal assumptions on the data, the Lipschitz continuity of the solution. Moreover a general duality theory is provided overcoming the difficulty of the voidness of the interior of the ordering cone which defines the cone constraints

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A Panoramic View on Projected Dynamical Systems

Cited by 2 publications

References 31 publications

Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization

Limit Behavior and the Role of Augmentation in Projected Saddle Flows for Convex Optimization

Lipschitz continuity and duality for dynamic oligopolistic market equilibrium problem with memory term

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