Computational, Combinatorial, and Geometric Aspects of Linear Optimization

线性优化的计算、组合和几何方面

• 批准号: RGPIN-2015-06163
• 负责人: Deza, Antoine
• 金额: $ 2.04万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=590884
• 关键词: Computational; Combinatorial; Geometric; Aspects; Linear

Rational decision-making through quantitative modelling and analysis is the guiding principle behind operations research, a field with several far-reaching applications across engineering, sciences, and industry. Finding optimal allocations of resources, scheduling tasks, and designing prototypes are a few of the areas operations research is concerned with. These problems can often be formulated, or approximated, as linear optimization problems, which involve maximizing or minimizing a linear function over a domain defined by a set of linear inequalities. The simplex and primal-dual interior point methods are currently the most computationally successful algorithms for linear optimization.

通过定量建模和分析进行理性决策是运筹学背后的指导原则，运筹学是一个在工程、科学和工业领域有着广泛应用的领域。寻找资源的最佳分配，调度任务，设计原型是运筹学关注的几个领域。这些问题通常可以公式化或近似为线性优化问题，其涉及在由一组线性不等式定义的域上最大化或最小化线性函数。单纯形法和原对偶内点法是目前求解线性优化问题的最成功的算法。