多目标分段线性分式规划的若干问题研究

项目名称： 多目标分段线性分式规划的若干问题研究

项目编号： No.11471230

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 方亚平

作者单位： 四川大学

项目金额： 68万元

中文摘要： 本项目对多目标分段线性分式规划中的如下几个问题进行研究:(1) 研究多目标分段线性分式规划的(弱)有效解集的结构和性质；（2）研究多目标分段线性分式规划的真有效解，给出其真有效解的刻画条件，讨论真有效解集与有效解集之间的关系；（3）研究数据是参数的光滑函数时，参数多目标分段线性分式规划的解映像的可微选择，从而建立多目标分段线性分式规划的灵敏性分析；（4）研究多目标分段线性分式规划的弱尖极小解性质以及弱尖极小解性质的稳定性；（5）研究求解多目标分段线性分式规划部分或全部解的迭代算法。这些问题的研究不仅可以丰富和发展多目标规划的理论、方法与技巧，而且可以为产生于财务管理、生产规划以及企业策划等领域中的大量决策问题的解决提供重要的理论依据，对学科和国民经济发展都有重要意义。

中文关键词： 多目标分段线性分式规划；解集的结构与性质；灵敏性分析；弱尖极小解；算法

英文摘要： In this project we study the following issues in multi-objective piecewise linear fractional programs: (1) We investigate the structures and properties of (weak) efficient solution sets of multi-objective piecewise linear fractional programs. (2) We study proper efficient solutions of multi-objective piecewise linear fractional programs by deriving some criteria for proper efficient solutions and discussing relations between the proper efficient solution set and the efficient solution set. (3) We attempt to establish sensitivity analysis in multi-objective piecewise linear fractional programs by investigating the differentiable selection of the solution map for a parametric multi-objective piecewise linear fractional program with smooth data depending upon a parameter. (4) We study the weak sharp solution and its stability in multi-objective piecewise linear fractional programs. (5) We develop methods to locate the set of part or all solutions of the multi-objective piecewise linear fractional program. The study on this project is important because it yields not only new theories and methods for multi-objective programs, but also provides tools for solving practical problems arising in financial planning, production planning, corporate planning, etc.

英文关键词： Multi-objective piecewise linear fractional program;Structure and property of solution sets;Sensitivity analysis;Weak sharp solution;Algorithm