Solving Strongly Monotone Variational and Quasi-Variational Inequalities

Nesterov, Yurii; Scrimali, Laura

doi:10.2139/ssrn.970903

Cited by 46 publications

(69 citation statements)

References 15 publications

(1 reference statement)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…For what regards QVIs there are a few works devoted to the numerical solution of finite-dimensional QVIs (see e.g. [10][11][12][13][14][15][16]); in particular in the recent paper [17] a solution method for QVIs based on solving their Karush-Kuhn-Tucker (KKT) conditions is proposed.…”

Section: Introductionmentioning

confidence: 99%

RETRACTED: Canonical dual approach for contact mechanics problems with friction

Latorre

Sagratella

Gao

2015

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

The following article has been included in a multiple retraction: Canonical Dual Approach for Contact Mechanics Problems with Friction; Vittorio Latorre, Simone Sagratella, David Y Gao. http://mms.sagepub.com/content/early/2015/01/20/1081286514566534.abstract In 2015 SAGE were made aware of concerns regarding the Special Issue of Mathematics & Mechanics of Solids on Advances in Canonical Duality Theory, guest-edited by Professor David Gao. At the request of the Guest Editor, the Special Issue has been retracted, due to conflict of interest regarding Professor Gao’s role as Guest Editor and co-author on a number of submitted papers. In addition the peer review process was less rigorous than the journal requires. The Guest Editor takes full responsibility for the retraction. The following articles that were due to appear in the Special Issue have therefore been retracted: Canonical Duality-Triality: Bridge between Nonconvex Analysis/Mechanics and Global Optimization in complex systems; David Y Gao, Ning Ruan, and Vittorio Latorre. http://mms.sagepub.com/content/early/2015/02/24/1081286514566533.abstract Canonical Dual Approach for Contact Mechanics Problems with Friction; Vittorio Latorre, Simone Sagratella, David Y Gao. http://mms.sagepub.com/content/early/2015/01/20/1081286514566534.abstract Canonical Duality Theory for Solving Non-Monotone Variational Inequality Problems; Guoshan Liu, David Y Gao, Shouyang Wang. http://mms.sagepub.com/content/early/2015/02/04/1081286514566535.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part I; Shu-Cherng Fang, David Y Gao, Gang-Xuan Lin, Ruey-Lin Sheu, Wen-Xun Xing. http://mms.sagepub.com/content/early/2015/02/24/1081286514566704.abstract Double Well Potential Function and Its Optimization in The n-dimensional Real Space. Part II; Yong Xia, Ruey-Lin Sheu, Shu-Cherng Fang, Wenxun Xing. http://mms.sagepub.com/content/early/2015/02/09/1081286514566723.abstract Analytic Solutions to 3-D Finite Deformation Problems Governed by St Venant-Kirchhoff Material; David Y Gao and E. Hajilarov. http://mms.sagepub.com/content/early/2015/07/06/1081286515591084.abstract Triality Theory and Complete Post-buckling Solutions of Large Deformed Beam by Canonical Dual Finite Element Method; Kun Cai, David Y Gao, Qinghua Qin. http://mms.sagepub.com/content/early/2015/06/28/1081286515591085.abstract Global Solutions to Spherically Constrained Quadratic Minimization via Canonical Duality Theory; Yi Chen, David Y Gao. http://mms.sagepub.com/content/early/2015/04/08/1081286515577122.abstract Unified Canonical Duality Methodology for Global Optimization; Vittorio Latorre, David Y Gao and N. Ruan. http://mms.sagepub.com/content/early/2015/07/06/1081286515591305.abstract A Framework of Canonical Dual Algorithms for Global Optimization; Xiaojun Zhou, David Y Gao, Chunhua Yang. http://mms.sagepub.com/content/early/2015/07/22/1081286515592190.abstract Canonical Duality Theory for Solving Nonconvex/Discrete Constrained Global Optimization Problems; Ning ...

show abstract

Section: Introductionmentioning

confidence: 99%

RETRACTED: Canonical dual approach for contact mechanics problems with friction

Latorre

Sagratella

Gao

2015

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

show abstract

“…where G : H → H is a positive symmetric linear operator were proposed by Fukushima (see for example [2], [7]). In [5] regularized gap functions were used for construction of methods for solving variational and quasi-variational inequalities.…”

Section: Gap Functions and Projection Measuresmentioning

confidence: 99%

“…So, r(z) can be used as a residual measure only for some classes of the variational inequalities (1). Let us start with one theorem related to one projection measure based on the methods and estimates from [5].…”

Section: Gap Functions and Projection Measuresmentioning

confidence: 99%

See 1 more Smart Citation

A posteriori bounds of approximate solution to variational and quasi-variational inequalities

Jacimovic

Krnic

2011

Filomat

View full text Add to dashboard Cite

In this paper we present some bounds of an approximate solution to variational and quasi-variational inequalities. The measures of errors can be used for construction of iterative and continuous procedures for solving variational (quasi-variational) inequalities and formulation of corresponding stopping rules. We will also present some methods based on linearization for solving quasi-variational inequalities.

show abstract

“…Different approaches have been considered to devise solution methods: characterizations based on fixed points and projections [13,51,52], penalization of coupling constraints [55,57,22], KKT systems [24], minimization of dual gap functions in the affine case [36]. Also Newton type methods, which guarantee only local convergence, have been developed [53,54].…”

Section: Introductionmentioning

confidence: 99%

Gap functions for quasi-equilibria

Bigi

Passacantando

2016

J Glob Optim

View full text Add to dashboard Cite

An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimates of its Clarke directional derivative is given. Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to guarantee that all the stationary points of a gap function actually solve QEP. A few classes of constraints satisfying such assumptions are identified covering a wide range of situations. Relying on these results, a descent method for solving QEP is devised and its convergence proved. Finally, error bounds are given in order to guarantee the boundedness of the sequence generated by the algorithm.

show abstract

Solving Strongly Monotone Variational and Quasi-Variational Inequalities

Cited by 46 publications

References 15 publications

RETRACTED: Canonical dual approach for contact mechanics problems with friction

RETRACTED: Canonical dual approach for contact mechanics problems with friction

A posteriori bounds of approximate solution to variational and quasi-variational inequalities

Gap functions for quasi-equilibria

Contact Info

Product

Resources

About