Behling, R., Lara, H., & Oviedo, H. (2023). Computing the completely positive factorization via alternating minimization. Numer. Linear Algebra Appl., Early Access.
Abstract: In this article, we propose a novel alternating minimization scheme for finding completely positive factorizations. In each iteration, our method splits the original factorization problem into two optimization subproblems, the first one being an orthogonal procrustes problem, which is taken over the orthogonal group, and the second one over the set of entrywise positive matrices. We present both a convergence analysis of the method and favorable numerical results.
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Kalahasthi, L., Holguin-Veras, J., & Yushimito, W. F. (2022). A freight origin-destination synthesis model with mode choice. Transp. Res. E-Logist. Transp. Rev., 157, 102595.
Abstract: This paper develops a novel procedure to conduct a Freight Origin-Destination Synthesis (FODS) that jointly estimates the trip distribution, mode choice, and the empty trips by truck and rail that provide the best match to the observed freight traffic counts. Four models are integrated: (1) a gravity model for trip distribution, (2) a binary logit model for mode choice, (3) a Noortman and Van Es' model for truck, and (4) a Noortman and Van Es' model for rail empty trips. The estimation process entails an iterative minimization of a nonconvex objective function, the summation of squared errors of the estimated truck and rail traffic counts with respect to the five model parameters. Of the two methods tested to address the nonconvexity, an interior point method with a set of random starting points (Multi-Start algorithm) outperformed the Ordinary Least Squared (OLS) inference technique. The potential of this methodology is examined using a hypothetical example of developing a nationwide freight demand model for Bangladesh. This research improves the existing FODS techniques that use readily available secondary data such as traffic counts and link costs, allowing transportation planners to evaluate policy outcomes without needing expensive freight data collection. This paper presents the results, model validation, limitations, and future scope for improvements.
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