Abstract The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature estimates that have harmful effects on the robustness of the iteration. In this paper, we propose a stochastic quasi-Newton method that is efficient, robust … Read more
We consider the task of classification in the high-dimensional setting where the number of features of the given data is significantly greater than the number of observations. To accomplish this task, we propose sparse zero-variance discriminant analysis (SZVD) as a method for simultaneouslyperforming linear discriminant analysis and feature selection on high-dimensional data. This method combines … Read more
This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ C_p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when … Read more
We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the cumulative mixture production up to that time. The mathematical formulation … Read more
A sharp upper bound on the probability of a random vector falling outside a polytope, based solely on the first and second moments of its distribution, can be computed efficiently using semidefinite programming. However, this Chebyshev-type bound tends to be overly conservative since it is determined by a discrete worst-case distribution. In this paper we … Read more
We study the problem of controlling multiple 2-D directional sensors while maximizing an objective function based on the information gain corresponding to multiple target locations. We assume a joint prior Gaussian distribution for the target locations. A sensor generates a (noisy) measurement of a target only if the target lies within the field-of-view of the … Read more
We consider a class of $\ell_0$-minimization problems, which is to search for the partial sparsest solution to an underdetermined linear system with additional constraints. We introduce several concepts, including $l_p$-induced quasi-norm ($0
Many practical problems can be formulated as $\ell_0$-minimization problems with nonnegativity constraints, which seek the sparsest nonnegative solutions to underdetermined linear systems. Recent study indicates that $\ell_1$-minimization is efficient for solving some classes of $\ell_0$-minimization problems. From a mathematical point of view, however, the understanding of the relationship between $\ell_0$- and $\ell_1$-minimization remains incomplete. In … Read more
In this paper we address the problem of identifying the most likely infection pattern responsible for the spread of a disease in a network. In particular, we focus on the scenario where limited information (i.e. infection reports) is available during an ongoing outbreak. For this problem we propose a maximum likelihood model and present an … Read more
Power System planning encompasses the concept of minimization of transmission losses keeping in mind the voltage stability and system reliability. Voltage profile decides the state of a system and its control is dependent on Generator source voltage, shunt/series injection, transformer taps etc. Optimal parameter setting in system level is needed for managing the available resources … Read more