Research Initiation: Interior Point Algorithms for Linear and Convex Programming

自从Karmarkar的线性规划算法发展以来，人们对求解线性规划和凸规划问题的内点算法重新产生了兴趣。内点算法的几个变种已经显示出与线性规划问题的单纯形法相比，在效率上有相当大的改进前景。通过这项建议，我们请求资金，以进一步研究这些算法的理论性质和计算效率。我们打算将我们以前工作中发展的理论与我们的实验经验有效地结合起来，开发一个通用的代码来解决这些问题。

Since the development of Karmarkar's algorithm for linear programming, interest is rejuvenated in the interior point algorithms for solving linear and convex programming problems. Several variants of interior point algorithms have shown considerable promise to achieve substantial improvement in efficiency over the simplex method for linear programming problems. Through this proposal, we request funds to further continue our study of the theoretical properties and the computational effectiveness of these algorithms. We intend to effectively integrate the theory developed in our previous work with our experimental experience to develop a general purpose code for solving these problems.^R JUSTIFICATION