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

几何规划是一种用于求解 某些代数类的非线性优化问题。 它 已经被应用于各种领域的问题，并已被 在工程设计中特别有用。 在这个项目中，一个 将分析几何规划的另一种方法 它用线性的原始-对偶对代替非线性的原始-对偶对， 相当于 具体而言，该项目将（1）开发，编码， 测试，并实现和算法的基础上的重新制定，（2） 将灵敏度分析程序从线性优化调整为 （3）采用线性规划分解 大型几何规划问题的原理， 可以基于设计变量划分约束集 （4）在几何上刻画多个最优解， 具有相同性质的问题;（5）探索近似 某些类别的一般非线性规划的几何 编程.

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.