Nonsmooth variational inequalities on Hadamard manifolds

Ansari, Qamrul Hasan; Islam, Monirul; Yao, Jen‐Chih

doi:10.1080/00036811.2018.1495329

Cited by 54 publications

(31 citation statements)

References 13 publications

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“…3 Yunnan University of Finance and Economics, Kunming, China. 4 College of Public Foundation, Yunnan Open University (Yunnan Technical College of National Defence Industry), Kunming 650500, China.…”

Section: Corollary 53 Letmentioning

confidence: 99%

“…The inverse variational inequalities were developed by He et al [1,2], which have many applications in various fields such as market equilibrium issues in economics, transportation networks and communication networks; see [3][4][5][6][7][8]. In 2014, Li et al [9] introduced a new class of inverse mixed variational inequality in the setting of Hilbert spaces, which has many applications in simple traffic network equilibrium control problems.…”

Section: Introductionmentioning

confidence: 99%

“…Sun and Chai [16] introduced regularized gap functions for generalized vector variation inequalities (GVVI) and obtained GVVI error bounds for regularized gap functions. Later on several authors studied the gap function for general variational inequality and Minty type variational inequality and demonstrate their error bounds by using the monotonicity in term of those gap functions; see [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Wu and Huang [17] implemented generalized f -projection operators to deal with mixed variational inequality.…”

Section: Introductionmentioning

confidence: 99%

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Error bounds for mixed set-valued vector inverse quasi-variational inequalities

et al. 2020

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The purpose of this paper is to introduce and study the mixed set-valued vector inverse quasi-variational inequality problems (MSVIQVIPs) and to obtain error bounds for this kind of MSVIQVIP in terms of the residual gap function, the regularized gap function, and the D-gap function. These bounds provide effective estimated distances between an arbitrary feasible point and the solution set of mixed set-valued vector inverse quasi-variational inequality problem. The results presented in the paper improve and generalize some recent results.

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Section: Corollary 53 Letmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Error bounds for mixed set-valued vector inverse quasi-variational inequalities

et al. 2020

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“…In many cases, these algorithms cannot obtain strong convergence; therefore, it was necessary to investigate new effective algorithms. Recently, several authors were able to apply the strong convergence of algorithms, see [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces

Almusawa

Hammad

Sharma³

2021

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In this manuscript, a new three-step iterative scheme to approximate fixed points in the setting of Busemann spaces is introduced. The proposed algorithms unify and extend most of the existing iterative schemes. Thereafter, by making consequent use of this method, strong and Δ-convergence results of mappings that satisfy the condition (Eμ) in the framework of uniformly convex Busemann space are obtained. Our results generalize several existing results in the same direction.

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“…In 2020, Ansari, Islam and Yao [1] are making one of the latest efforts to relate variational and optimization problems where they have tested some existence results for non-smooth variational inequality problem and Minty non-smooth variational inequality problem using fixed point theorem on Hadamard manifolds. So, the topic of this article is hot.…”

Section: Introductionmentioning

confidence: 99%

Vectorial Variational Inequalities on Hadamard Manifolds: A Tool to Achieve Efficient Approximate Solutions

Garzón¹,

Osuna-Gómez²,

Rufián-Lizana³

et al. 2020

Preprint

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This article has two objectives. Firstly, we will use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of Vector Optimization Problem within the novel field of the Hadamard manifolds. Previously, we will introduce the concepts of generalized approximate geodesic convex functions and illustrate them with examples. We will see the minimum requirements under which critical points, solutions of Stampacchia and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we will show an economical application, using again solutions of the variational problems to identify with Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions.

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Nonsmooth variational inequalities on Hadamard manifolds

Cited by 54 publications

References 13 publications

Error bounds for mixed set-valued vector inverse quasi-variational inequalities

Error bounds for mixed set-valued vector inverse quasi-variational inequalities

Approximation of the Fixed Point for Unified Three-Step Iterative Algorithm with Convergence Analysis in Busemann Spaces

Vectorial Variational Inequalities on Hadamard Manifolds: A Tool to Achieve Efficient Approximate Solutions

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