In this study, we introduce a distribution network design problem that determines the locations and capacities of the relief distribution points in the last mile network, while considering demand- and network-related uncertainties in the post-disaster environment. The problem addresses the critical concerns of relief organizations in designing last mile networks, which are providing accessible and … Read more
With the need of 16/11nm cells, triple patterning lithography (TPL) has been concerned in lithography industry. Based on a new conflict projection technique to identify conflicts, we formulate in this paper the TPL layout decomposition problem as a minimum cost coloring problem. The problem is solved in two steps. First, it is relaxed to a … Read more
In this paper, we consider the polyhedral structure of the integrated minimum-up/-down time and ramping polytope for the unit commitment problem. Our studied generalized polytope includes minimum-up/-down time constraints, generation ramp-up/-down rate constraints, logical constraints, and generation upper/lower bound constraints. We derive strong valid inequalities by utilizing the structures of the unit commitment problem, and … Read more
Variable selection is a fundamental task in statistical data analysis. Sparsity-inducing regularization methods are a popular class of methods that simultaneously perform variable selection and model estimation. The central problem is a quadratic optimization problem with an $\ell_0$-norm penalty. Exactly enforcing the $\ell_0$-norm penalty is computationally intractable for larger scale problems, so different sparsity-inducing penalty … Read more
In this paper we analyze boosting algorithms in linear regression from a new perspective: that of modern first-order methods in convex optimization. We show that classic boosting algorithms in linear regression, namely the incremental forward stagewise algorithm (FS-epsilon) and least squares boosting (LS-Boost-epsilon), can be viewed as subgradient descent to minimize the loss function defined … Read more
This paper proposes three strong second order cone programming (SOCP) relaxations for the AC optimal power flow (OPF) problem. These three relaxations are incomparable to each other and two of them are incomparable to the standard SDP relaxation of OPF. Extensive computational experiments show that these relaxations have numerous advantages over existing convex relaxations in … Read more
The ensemble density functional theory is valuable for simulations of metallic systems due to the absence of a gap in the spectrum of the Hamiltonian matrices. Although the widely used self-consistent field iteration method can be extended to solve the minimization of the total energy functional with respect to orthogonality constraints, there is no theoretical … Read more
The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The rst one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The … Read more
In packing problems with fragmentation a set of items of known weight is given, together with a set of bins of limited capacity; the task is to find an assignment of items to bins such that the sum of items assigned to the same bin does not exceed its capacity. As a distinctive feature, items … Read more
We consider inverse problems in atmospheric modelling. Instead of using the ordinary least squares, we add a weighting matrix based on the topology of measurement points and show the connection with Bayesian modelling. Since the source–receptor sensitivity matrix is usually ill-conditioned, the problem is often regularized, either by perturbing the objective function or by modifying … Read more