Study On Image Space Analysis Of Optimization Problem By Virtue Of Scalarization Function

This paper mainly studies the optimization problem by utilizing image spaceanalysis approach.In Chapter1, we introduce research survey of vector problem and image spaceanalysis approach.In Chapter2, by virtue of a nonlinear scalarization function, two nonlinear weakseparation functions, a nonlinear regular weak separation function, and a nonlinearstrong separation function are first introduced. Then image space analysis approach wasapplied to the discussion of vector optimization problem with constraints, and wepromote the conclusions of corresponding literature by illustrating some examples.In Chapter3, a nonlinear weak separation function and a nonlinear regular weakseparation function are first introduced by employing the nonlinear scalarizationfunction. Then image space analysis approach was applied to the discussion ofoptimality conditions, gap function of weak vector equibrium problem. Then byutilizing the gap function, we obtain error bound of weak vector equibrium problem.In Chapter4, we study optimality conditions of quasi-variational inequality problemwith cone constraints by virtue of the image space analysis. By using a nonlinearscalarization function and a positive linear operator, a nonlinear regular weak separationfunction, a nonlinear weak separation function, a nonlinear strong separation functionand a linear regular weak separation function are constructed. By using these separationfunctions, we obtain some optimality conditions of quasi-variational inequality problemwith cone constraints.In Chapter5, we make a brief summary and outlook.