Gerstewitz非线性标量化函数的性质及其在向量优化中的应用

Properties of Gerstewitz Nonlinear Scalarization Function and Applications in Vector Optimization

【目的】对Gerstewitz非线性标量化函数的性质作进一步研究与应用。【方法】利用代数内部和向量闭包研究Gerstewitz非线性标量化函数的一些性质。【结果】给出了Gerstewitz非线性标量化函数的一些性质,进而利用这些性质建立了集值向量优化问题有效点和弱有效点的非线性标量化结果。【结论】将拓扑内部推广到代数内部情形,推广了Gerstewitz非线性标量化函数的一些性质与应用。

[Purposes]The properties and applications of Gerstewitz nonlinear scalarization function are studied further.[Methods]Using the algebraic interior and the vector closure,some properties of Gerstewitz nonlinear scalarization function are studied.[Findings]Some properties are given for the Gerstewitz nonlinear scalarization function and some nonlinear scalarization results of（weakly）efficient points are established by making use of these properties for a class of vector optimization problems with set-valued maps.[Conclusion]Some results in the sense of topological interior are generalized to the case of algebraic interior,and some properties and applications of Gerstewitz nonlinear scalarization function are generalized.