Large-Scale Symmetric Cone Programming with Applications in Mine Planning

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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.