Large-Scale Symmetric Cone Programming with Applications in Mine Planning

对称锥规划是最小化受线性约束的线性形式的过程，并且附加要求该点在对称锥中。对称锥规划在科学、工程、经济、金融等领域有着广泛的应用，其中包括组合优化和控制理论的一些突破。 目前，大多数对称锥规划问题都是用内点法求解的，但由于每次迭代都需要大量的计算机内存和CPU资源来计算，因此不能应用于大规模问题。 在这个研究项目中，我们将根据对称锥的特殊结构和性质，设计求解大规模对称锥规划问题的有效方法。我们的方法在理论上是收敛的，在实际中是有效的。我们提出的方法的每一次迭代都将是廉价的。与现有方法相比，我们提出的方法将在更短的时间内获得更大问题的更准确的解。由于对称锥规划的广泛应用，我们的研究将造福于整个社会。 我们将把我们的大规模对称锥规划方法应用到矿山规划中。将矿价的不确定性融入到矿山规划模型中，并用我们提出的大规模对称锥规划方法对模型进行求解。本文的研究将为矿山规划决策提供有益的参考。鉴于一个矿山项目投资巨大，矿业投资决策稍有改进，将为矿业节省数百万美元。加拿大的采矿业将从我们提议的研究中受益。

Symmetric cone programming is the process of minimizing a linear form subject to linear constraints and an additional requirement that the point be in a symmetric cone. Symmetric cone programming has a wide applications in a variety of areas in science, engineering, economics, and finance, including some breakthroughs in combinatorial optimization and control theory. Currently, most symmetric cone programming problems are solved by interior-point methods(IPMs); however, IPMs cannot be applied to large-scale problems, because each iteration of an IPM requires a lot of computer memory and CPU resources to compute. In this research program, we will design efficient methods for large-scale symmetric cone programming problems based on the special structures and properties of symmetric cones. Our methods will be theoretically convergent and practically efficient. Each iteration of our proposed methods will be cheap. Our proposed methods will obtain more accurate solutions for larger problems in less time than existing methods do. Because of the vast applications of symmetric cone programming, our research will benefit society as a whole. We will apply our large-scale symmetric cone programming methods to mine planning. we will incorporate uncertainty of mineral prices in mine planning models, and solve the resulting model by our proposed large-scale symmetric cone programming methods. Our research will improve the decision-making for mine planning. In view of huge investment in a mine project, a small improvement in mining investment decision-making will save the mining industry millions of dollars. Canada's mining industry will benefit from our proposed research.