This paper is concerned with the cross-validation criterion for best subset selection in a linear regression model. In contrast with the use of statistical criteria (e.g., Mallows’ $C_p$, AIC, BIC, and various information criteria), the cross-validation only requires the mild assumptions, namely, samples are identically distributed, and training and validation samples are independent. For this … Read more
Economic dispatch (ED) problem considering valve-point effects (VPE), transmission loss and prohibited operating zones (POZ) is a very challenging issue due to its intrinsic non-convex, non-smooth and non-continuous natures. To achieve a near globally solution, a fully mixed-integer linear programming (FMILP) formulation is proposed for such an ED problem. Since the original loss function is … Read more
Sufficient conditions are provided for a deterministic algorithm for estimating an L1-norm best-fit one-dimensional subspace. To prove the conditions are sufficient, fundamental properties of the L1-norm projection of a point onto a one-dimensional subspace are derived. Also, an equivalence is established between the algorithm, which involves the calculation of several weighted medians, and independently-derived algorithms … Read more
This paper examines multi-interval real-time markets in the context of US independent system operators (ISOs). We show that current ISO implementations that settle only the upcoming interval of the multi-interval solution can create incentive problems. Fundamentally, this is the result of each successive optimization problem treating historical losses as sunk costs. To solve the incentive … Read more
We present a detailed set of performance comparisons of two state-of-the-art solvers for the application of designing time-delay compensators, an important problem in the field of robust control. Formulating such robust control mechanics as constrained optimization problems often involves objective and constraint functions that are both nonconvex and nonsmooth, both of which present significant challenges … Read more
This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control. Numerical experiments are presented indicating that the use … Read more
In this paper, we consider the recovery of group sparse signals corrupted by impulsive noise. In some recent literature, researchers have utilized stable data fitting models, like $l_1$-norm, Huber penalty function and Lorentzian-norm, to substitute the $l_2$-norm data fidelity model to obtain more robust performance. In this paper, a stable model is developed, which exploits … Read more
We develop a two-stage stochastic program for energy and reserve dispatch, which ensures the safe operation of a power system with a high penetration of renewables and a strong interdependence with the natural gas system. Distributionally robust joint chance constraints with Wasserstein ambiguity sets ensure that there is no need for load shedding and renewable … Read more
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present … Read more
We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the $\ell_0$ pseudo–norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm $\|.\|_{[k]}$, intermediate … Read more