Optimization problems are considered that involve 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 materials science among others, and are known to be NP-hard for a special case of interest. The underlying structure of such optimization problems is analysed for two particular applications and, depending on the matrix family, compact-size mixed-integer linear or quadratically constrained quadratic programming reformulations are obtained that can be solved via commercial solvers. Finally, the results are presented of computational experiments that demonstrate the success of the author's approach compared to heuristic and enumeration methods predominant in the literature.

考虑的优化问题涉及从给定族中选择的变量矩阵的乘法，这可能是离散集、连续集或两者的组合。这种非线性且可能是离散的优化问题出现在生物学和材料科学等领域的应用中，并且已知对于感兴趣的特殊情况是 NP 难的。针对两个特定应用分析了此类优化问题的底层结构，并根据矩阵族，获得了可以通过商业求解器求解的紧凑大小的混合整数线性或二次约束二次规划重构。最后，展示了证明作者成功的计算实验的结果。