论文标题
涉及矩阵乘法与材料科学和生物学应用的优化问题
Optimization Problems Involving Matrix Multiplication with Applications in Material Science and Biology
论文作者
论文摘要
我们考虑涉及要从给定家族中选择的可变矩阵的乘法的优化问题，这可能是离散集，连续集或两者的组合。这种非线性以及可能的离散性问题在生物学和材料科学等应用中出现，并且众所周知，对于特殊的感兴趣而言，这是NP-HARD。我们分析了两个特定应用的此类优化问题的潜在结构，并取决于基质家族，获得了可以通过商业溶解器解决的紧凑型混合量线性或四次约束二次编程重新纠正。最后，我们介绍了计算实验的结果，该结果证明了我们的方法与文献中主要的启发式和枚举方法相比的成功。
We consider optimization problems involving the multiplication of variable matrices to be selected from a given family, which might be a discrete set, a continuous set or a combination of both. Such nonlinear, and possibly discrete, optimization problems arise in applications from biology and material science among others, and are known to be NP-Hard for a special case of interest. We analyze the underlying structure of such optimization problems for two particular applications and, depending on the matrix family, obtain compact-size mixed-integer linear or quadratically constrained quadratic programming reformulations that can be solved via commercial solvers. Finally, we present the results of our computational experiments, which demonstrate the success of our approach compared to heuristic and enumeration methods predominant in the literature.
