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Advances in mathematical optimization for machine learning and data analysis – Part III

**FD-02: Advances in mathematical optimization for machine learning and data analysis – Part III**

Stream: Advances in mathematical optimization for machine learning

Room: Turing

Chair(s): Dimitri Papadimitriou

Mixed integer optimization in ARMA models

Leonardo Di Gangi

Model selection and fitting represent two critical aspects of Auto Regressive Moving Average (ARMA) models. It is proposed an algorithm which performs the selection and estimation of ARMA models as a single optimization routine without any statistical knowledge. The computational core of the algorithm is based on a two-step Gauss-Seidel decomposition scheme, where at each iteration the first step involves the update of the autoregressive and moving average parameters by solving a Mixed Integer Optimization problem and the second step the closed form update of the variance parameter.

Model of Optimal Centroids Approach For Multivariate Data Classification

Pham Van Nha, Le Cam Binh

Particle swarm optimization-PSO is a well-known multidisciplinary optimization algorithm. However, the general mathematical model of PSO has not been presented. In this paper, PSO will be presented as a general mathematical model and applied in multivariate data classification. First, PSO’s the general mathematical model is analyzed so that can be applied into complex applications. Then, Model of Optimal Centroids-MOC is proposed for multivariate data classification. Experiments were conducted on some data sets to demonstrate the effectiveness of MOC compared with some proposed algorithms

IGLOO: A stochastic global optimization algorithm to predict the structure of biomolecules adsorbed on metal surfaces

Juan CORTES, Nathalie TARRAT, Christian Schoen

Predicting conformations of molecular systems constitutes a global optimization problem for an appropriate cost (energy) function, where not only the global minimum but also a representative set of local minima is expected as output. Depending on the system size and the complexity of the energy function, solving this optimization problem can be extremely challenging. Our proposed Iterative Global exploration and LOcal Optimization (IGLOO) algorithm iterates RRT-based sampling, local minimization and clustering, until convergence is achieved. We show its performance in a real application.