多参数正项几何规划问题
Posynomial Geometric Programming Problems with Multiple Parameters
摘要：
几何规划问题是求解某些特殊类型非线性规划问题的有力工具。它在优化和工程中有广泛的应用，可以解决一些复杂的优化问题。几何规划的许多应用是在工程设计问题中，其中参数估计使用几何规划。当问题中的参数不精确时，计算的目标值也不精确。本文提出了一种求解目标函数中变量的指数、代价系数和右端均为多参数的几何规划问题的方法。利用对偶定理，建立了求解目标函数值的等价数学规划问题。应用变量可分离技术，将多选择数学规划问题转化为多个一层几何规划问题，从而产生多个目标值，帮助工程师处理更符合实际的工程设计问题。
英文摘要：
Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many applications of geometric programming are on engineering design problems where parameters are estimated using geometric programming. When the parameters in the problems are imprecise, the calculated objective value should be imprecise as well. In this paper we have developed a method to solve geometric programming problems where the exponent of the variables in the objective function, cost coefficients and right hand side are multiple parameters. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem. By applying a variable separable technique the multi-choice mathematical programming problem is transformed into multiple one level geometric programming problem which produces multiple objective values that helps engineers to handle more realistic engineering design problems.
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