In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended formulation. Then, using the convex hull description for the bivariate case as a building block, we derive … Read more
Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more
The thermal unit commitment (UC) problem often can be formulated as a mixed integer quadratic programming (MIQP), which is difficult to solve efficiently, especially for large-scale instances. The tighter characteristic re-duces the search space, therefore, as a natural conse-quence, significantly reduces the computational burden. In the literature, many tightened formulations for single units with parts … Read more
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic Unit Cell (PUC) and the efficacy of non-uniform designs in multi-scale material optimization. Here, we introduce a novel strategy for concurrent minimum-compliance design of … Read more
Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs. In the proposed method, the barrier parameter is updated in every step as done in interior-point methods for linear programs, which is prominently different from the existing interior-point methods … Read more
Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such is social network analysis and computational biology. There is a significant amount of literature studying this problem under the assumption that the communities … Read more
We investigate the problem of exactly separating cover inequalities of maximum depth and we develop a pseudo-polynomial-time algorithm for this purpose. Compared to the standard method based on the maximum violation, computational experiments carried out on knapsack and multi-dimensional knapsack instances show that, with a cutting-plane method based on the maximum-depth criterion, we can optimize … Read more
In critical node problems, the task is identify a small subset of so-called critical nodes whose deletion maximally degrades a network’s “connectivity” (however that is measured). Problems of this type have been widely studied, e.g., for limiting the spread of infectious diseases. However, existing approaches for solving them have typically been limited to networks having … Read more
We consider the least squares regression problem, penalized with a combination of the L0 and L2 norms (a.k.a. L0 L2 regularization). Recent work presents strong evidence that the resulting L0-based estimators can outperform popular sparse learning methods, under many important high-dimensional settings. However, exact computation of L0-based estimators remains a major challenge. Indeed, state-of-the-art mixed … Read more
The Double Row Layout Problem (DRLP) occurs in automated manufacturing environments, where machines arranged in a double-row layout, i.e. the machines are located on either side of a straight line corridor. The DRLP is how to minimize the total cost of transporting materials between machines. The problem is NP-Hard. In this paper, we give a … Read more