论文标题
指示变量的约束凸优化问题的理想配方
Ideal formulations for constrained convex optimization problems with indicator variables
论文作者
论文摘要
在本文中，我们研究了指标变量和指标的组合约束，我们研究了一类凸优化问题的凸面化。与以前关于稀疏回归问题的启动性的大多数工作不同，我们同时考虑了非线性的不可分割的目标，指标变量和组合约束。具体而言，我们给出了在任意组合约束下的一维凸函数的题词和仿射函数的凸面描述。作为这种结果的特殊情况，我们为层次结构，多重共线性和稀疏性约束的问题提供了理想的凸质。此外，我们还提供了一个简短的证据，即对于可分离的目标函数，观点重新构造与问题的限制无关。我们在实际数据集的层次结构约束下进行回归问题的计算实验证明了拟议方法在没有大量计算开销的情况下改善放松质量的潜力。
Motivated by modern regression applications, in this paper, we study the convexification of a class of convex optimization problems with indicator variables and combinatorial constraints on the indicators. Unlike most of the previous work on convexification of sparse regression problems, we simultaneously consider the nonlinear non-separable objective, indicator variables, and combinatorial constraints. Specifically, we give the convex hull description of the epigraph of the composition of a one-dimensional convex function and an affine function under arbitrary combinatorial constraints. As special cases of this result, we derive ideal convexifications for problems with hierarchy, multi-collinearity, and sparsity constraints. Moreover, we also give a short proof that for a separable objective function, the perspective reformulation is ideal independent from the constraints of the problem. Our computational experiments with regression problems under hierarchy constraints on real datasets demonstrate the potential of the proposed approach in improving the relaxation quality without significant computational overhead.
