Second-order cone programming is a highly tractable convex optimization class. In this paper, we fit general second-order cone constraints to data. This is of use when one must solve large-scale, nonlinear optimization problems, but modeling is either impractical or does not lead to second-order cone or otherwise tractable constraints. Our motivating application is biochemical process optimization, in which we seek to fit second-order cone constraints to microbial growth data. The fitting problem is nonconvex. We solve it using the concave–convex procedure, which takes the form of a sequence of second-order cone programs. We validate our approach on simulated and experimental microbial growth data, and compare its performance with conventional nonlinear least-squares fitting.

二阶锥规划是一种高度易处理的凸优化类。在本文中，我们将一般的二阶锥约束拟合到数据中。当必须解决大规模非线性优化问题，但建模要么不切实际，要么不会导致二阶锥体或其他易处理的约束时，这很有用。我们的激励应用是生化过程优化，其中我们寻求将二阶锥约束拟合到微生物生长数据。拟合问题是非凸的。我们使用凹凸过程来解决它，它采用一系列二阶锥程序的形式。我们在模拟和实验微生物生长数据上验证了我们的方法，并将其性能与传统的非线性最小二乘拟合进行了比较。