Unconstrained optimization reformulations of equilibrium problems

DOI10.1007/s10114-008-7096-1zbMath1206.90185OpenAlexW2405903239MaRDI QIDQ1034258

Ji-ye Han, Li-ping Zhang

Publication date: 11 November 2009

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-008-7096-1

zbMATH Keywords

unconstrained optimizationerror boundequilibrium problemsD-gap function

Mathematics Subject Classification ID

Nonlinear programming (90C30) Sensitivity, stability, parametric optimization (90C31) Nonsmooth analysis (49J52) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items (13)

Mixed equilibrium problems with \(Z^*\)-bifunctions and least element problems in Banach lattices ⋮ An algorithm based on the generalized D-gap function for equilibrium problems ⋮ A convergent inexact solution method for equilibrium problems ⋮ Twelve monotonicity conditions arising from algorithms for equilibrium problems ⋮ Gap functions and penalization for solving equilibrium problems with nonlinear constraints ⋮ Error bounds of regularized gap functions for nonmonotone Ky Fan inequalities ⋮ Differentiated oligopolistic markets with concave cost functions via Ky Fan inequalities ⋮ Merit functions: a bridge between optimization and equilibria ⋮ Merit functions: a bridge between optimization and equilibria ⋮ A note on D-gap functions for equilibrium problems ⋮ On some approaches to find Nash equilibrium in concave games ⋮ Descent and penalization techniques for equilibrium problems with nonlinear constraints ⋮ D-gap functions and descent techniques for solving equilibrium problems

Cites Work

• Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems
• Theoretical and numerical investigation of the D-gap function for box constrained variational inequalities
• A general descent framework for the monotone variational inequality problem
• An extended descent framework for variational inequalities
• Unconstrained optimization reformulations of variational inequality problems
• Equivalence of variational inequality problems to unconstrained minimization
• Gap functions for equilibrium problems
• Convergence of hybrid steepest-descent methods for generalized variational inequalities
• Superlinear/quadratic one-step smoothing Newton method for \(P_0\)-NCP
• Variational principles for variational inequalities
• D-gap Functions for a Class of Equilibrium Problems in Banach Spaces

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