Research Initiation Award: Investigation in an Alternative Approach to Geometric Programming

几何规划是解决某些代数、非线性优化问题的一种成熟技术。它已被应用于各种领域的问题，在工程设计中尤其有用。在这个项目中，将分析一种替代几何规划的方法，用线性等效对取代非线性原对偶对。具体而言，该项目将(1)开发、编码、测试和实现基于重新表述的算法，(2)将灵敏度分析程序从线性优化调整到几何规划，(3)将线性规划分解原理调整到大型几何规划问题，其中约束集可以根据其中出现的设计变量进行划分，(4)刻画具有相同性质的几何问题中的多个最优解；(5)探索用几何规划逼近一类一般非线性规划。

Geometric Programming is an established technique for solving certain classes of algebraic, nonlinear optimization problems. It has been applied to problems in a variety of areas, and has been especially useful in engineering design. In this project, an alternative approach to geometric programming will be analyzed which replaces the nonlinear primal-dual pair with a linear equivalent. Specifically, the project will (1) develop, code, test, and implement and algorithm based on the reformulation,(2) adapt sensitivity analysis procedures from linear optimization to geometric programming, (3) adapt linear programming decomposition principles to large geometric programming problems where the constraint sets can be partitioned based on the design variables that appear in them, (4) characterize multiple optima in geometric problems which possess the same, and (5) explore the approximation of certain classes of general nonlinear programs by geometric programming.