In this papert we construct unconstrained methods for the generalized nonlinearcomplementarity problem and variational inequalities. Properties of the correspon-dent unconstrained optimization problem are studied. We ...In this papert we construct unconstrained methods for the generalized nonlinearcomplementarity problem and variational inequalities. Properties of the correspon-dent unconstrained optimization problem are studied. We apply these methods tothe subproblems in trust region method, and study their interrelationships. Nu-merical results are also presented.展开更多
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
指出了P.Katchang等人的论文[Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method,Nonlinear Analysis:Hybrid Systems,2010,4:83...指出了P.Katchang等人的论文[Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method,Nonlinear Analysis:Hybrid Systems,2010,4:838-852]在主要收敛性定理的证明过程中使用了两个不正确的不等式,因而导致证明过程不严谨。本文给出了该定理的一个正确证明。展开更多
文摘In this papert we construct unconstrained methods for the generalized nonlinearcomplementarity problem and variational inequalities. Properties of the correspon-dent unconstrained optimization problem are studied. We apply these methods tothe subproblems in trust region method, and study their interrelationships. Nu-merical results are also presented.
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
文摘指出了P.Katchang等人的论文[Strong convergence theorems for solving generalized mixed equilibrium problems and general system of variational inequalities by the hybrid method,Nonlinear Analysis:Hybrid Systems,2010,4:838-852]在主要收敛性定理的证明过程中使用了两个不正确的不等式,因而导致证明过程不严谨。本文给出了该定理的一个正确证明。
