求解多值广义混合隐似平衡问题的迭代算法

Iterative Algorithm for Solving Multivalued Generalized Mixed Implicit Quasi-Equilibrium Problems

引入和研究了一类新的多值广义混合隐似平衡问题,这类平衡问题包含了许多已知的广义混合隐似变分不等式问题和广义平衡问题作为特例,同时也引进了新概念局部松弛N-g-联合伪单调.运用辅助原理技巧提出和分析了求解这类多值广义混合隐似平衡问题的预测校正迭代算法.所提出算法的收敛性仅需要映射的连续性和局部松弛N-g-联合伪单调.

A new class of multivalued generalized mixed implicit quasi-equilibrium problems are introduced and studied.The class includes many known generalized mixed implicit quasi-variational inequality problems and generalized equilibrium problems as many special cases.For solving these problems,a new definition of partially relaxed N-g-jointly pseudomonotonicity is introduced and a new predictor-corrector iterative algorithm is suggested and analyzed by using the auxiliary principle technique.The convergence of the suggested algorithm only requires the continuity and the partially relaxed N-g-jointly pseudomonotonicity of the mappings.