Solving variational inequality and fixed point problems by line searches and potential optimization
From MaRDI portal
Publication:1764238
DOI10.1007/s10107-003-0476-5zbMath1073.90051OpenAlexW2007833245MaRDI QIDQ1764238
Georgia Perakis, Thomas L. Magnanti
Publication date: 24 February 2005
Published in: Mathematical Programming. Series A. Series B (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10107-003-0476-5
Variational inequalitiesFixed point problemsAveraging schemesNonexpansive mapsStrongly-f-monotone maps
Variational inequalities (49J40) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)
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Cites Work
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- Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications
- A note on a globally convergent Newton method for solving monotone variational inequalities
- On the weak convergence of an ergodic iteration for the solution of variational inequalities for monotone operators in Hilbert space
- Ergodic convergence to a zero of the sum of monotone operators in Hilbert space
- Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- On recursive averaging processes and Hilbert space extensions of the contraction mapping principle
- The computation of fixed points and applications
- Conditional gradient algorithms with open loop step size rules
- A general descent framework for the monotone variational inequality problem
- Modified descent methods for solving the monotone variational inequality problem
- A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
- On the convergence of projection methods: Application to the decomposition of affine variational inequalities
- A unifying geometric solution framework and complexity analysis for variational inequalities
- Network economics: a variational inequality approach
- Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming
- A globally convergent Newton method for solving strongly monotone variational inequalities
- Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
- Construction of fixed points of nonlinear mappings in Hilbert space
- Construction of a fixed point for contractions in Banach space
- Methodes itératives pour les équations et inéquations aux dérivées partielles non linéaires de type monotone. (Iteration methods for nonlinear equations and inequations with partial derivatives of monotone type)
- The Orthogonality Theorem and the Strong-f-Monotonicity Condition for Variational Inequality Algorithms
- Recurrence of nonexpansive mappings in Banach spaces
- Projected gradient methods for linearly constrained problems
- AN ITERATIVE METHOD FOR VARIATIONAL INEQUALITIES WITH APPLICATION TO TRAFFIC EQUILIBRIUM PROBLEMS
- Generalized Descent Methods for Asymmetric Systems of Equations
- Newton’s Method and the Goldstein Step-Length Rule for Constrained Minimization Problems
- Convergence Rates for Conditional Gradient Sequences Generated by Implicit Step Length Rules
- Global and Asymptotic Convergence Rate Estimates for a Class of Projected Gradient Processes
- Iterative methods for variational and complementarity problems
- Fixed Points and Iteration of a Nonexpansive Mapping in a Banach Space
- Monotone Operators and the Proximal Point Algorithm
- Averaging Schemes for Variational Inequalities and Systems of Equations
- An iterative scheme for variational inequalities
- Finite-Dimensional Variational Inequalities and Complementarity Problems
- Co-Coercivity and Its Role in the Convergence of Iterative Schemes for Solving Variational Inequalities
- Partially Asynchronous, Parallel Algorithms for Network Flow and Other Problems
- Fixed points of nonexpanding maps
