Issues Relating Linear Programming, Complexity Theory and Numeric Computation

主要目标涉及发展和 用复杂性理论分析线性规划的算法 基于功能分析而不是传统的 受代数和组合学的启发 特别注意 鉴于计算机舍入误差和数据不准确的问题， 问题，如如何使用一个人的先验知识， 为了有效地解决问题， 问题使用较少的计算精度比将需要否则。 的 使用迭代方法求解方程时， 方法进行了调查，因为这是可能的， 算法是（近）最优的;研究了最优性 通过近似理论。 线性摄动理论 正在拟订方案。 某些概念已被证明是有用的， 线性规划的背景正在更一般的背景下进行研究 多变量多项式 它的目的是， 调查工作将尽可能具有一般性; 例如，定义非负性的圆锥体将不需要被 多面体的

The primary objectives concern the development and analysis of algorithms for linear programming within a complexity theory motivated by functional analysis rather than the traditional motivated by algebra and combinatorics. Special attention is given to issues concerning computer round-off error and inexact data, issues such as how one might use the prior knowledge one has regarding the structure of the problem to be solved in order to efficiently solve the problem using less computational precision than would be needed otherwise. The use of iterative methods for solving the equations that arise when applying methods is investigated, as is the possibility that the algorithms are (nearly) optimal; optimality is investigated via approximation theory. Perturbation theory for linear programming is being developed. Certain notions which have proven useful in the context of linear programming are being investigated in a more general context multi-variate polynomials. It is intended that all of the investigations will be carried out with as much generality as is possible; for example, the cones defining non-negativity will not be required to be polyhedral.