A dynamical system for solving inverse quasi-variational inequalities

Dey, Soumitra; Reich, Simeon

doi:10.1080/02331934.2023.2173525

Cited by 7 publications

(5 citation statements)

References 24 publications

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“…For the applications, formulation, sensitivity, dynamical systems, generalizations, and other aspects of the variational inequalities, see [6,7,[12][13][14][15][16][17]20,23,25,26,[28][29][30][32][33][34][35][36][37][38][40][41][42][43][44][45][46][48][49][50][51][52][53][54][55][56]58,61,63] and the references therein.…”

Section: Formulations and Basic Factsmentioning

confidence: 99%

“…If T = I, the identity operator, then problem (2.6)is called the inverse quasi variational inequalities, see [13], that is, finding µ ∈ Ω(µ), such that…”

Section: Definition 23 [44]mentioning

confidence: 99%

“…It has been shown that the dynamical systems are useful in developing some efficient numerical techniques for solving variational inequalities and related optimization problems. For more details, see [13,14,41,50,54,66,67]. We consider some iterative methods for solving the quasi variational inequalities.…”

Section: Dynamical Systems Techniquementioning

confidence: 99%

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Recent Developments in General Quasi Variational Inequalities

AlShejari,

Noor,

Noor

2024

Int. J. Anal. Appl.

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In this paper, we present a number of new and known numerical techniques for solving general quasi variational inequalities, introduced by Noor [34] in 1988, using various techniques including projection, Wiener-Hopf equations, auxiliary principle, dynamical systems coupled with finite difference approach and sensitivity analysis. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. Some special cases are discussed as applications of the main results. Several open problems are suggested for future research.

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Section: Formulations and Basic Factsmentioning

confidence: 99%

“…If T = I, the identity operator, then problem (2.6)is called the inverse quasi variational inequalities, see [13], that is, finding µ ∈ Ω(µ), such that…”

Section: Definition 23 [44]mentioning

confidence: 99%

See 1 more Smart Citation

Recent Developments in General Quasi Variational Inequalities

AlShejari,

Noor,

Noor

2024

Int. J. Anal. Appl.

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“…Additionally, several discretization strategies were also provided to derive the discrete-time form. For more details about analyzing and designing optimization algorithms using control theory, one may refer to [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

“…As we have declared before, the exact fixed-time convergence to the minimum point cannot be achieved since FTGD ( 13) is singular when ∇ f (x) = 0, and algorithm (18) can then be applied. 13) and FTGD in [22]: (a) convergence results for FTGD (13) (b) convergence results for FTGD in [22].…”

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confidence: 99%

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Chen,

Sun,

Wang

2023

Mathematics

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Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness.

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Regularized dynamics for monotone inverse variational inequalities in hilbert spaces

Anh,

Hai

2024

Optim Eng

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A dynamical system for solving inverse quasi-variational inequalities

Cited by 7 publications

References 24 publications

Recent Developments in General Quasi Variational Inequalities

Recent Developments in General Quasi Variational Inequalities

Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme

Regularized dynamics for monotone inverse variational inequalities in hilbert spaces

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