Data Science Applications

Almost-sure convergence of iterates and multipliers in stochastic sequential quadratic optimization

Categories Constrained Nonlinear Optimization, Data Science Applications, Stochastic Programming Tags , , ,

Stochastic sequential quadratic optimization (SQP) methods for solving continuous optimization problems with nonlinear equality constraints have attracted attention recently, such as for solving large-scale data-fitting problems subject to nonconvex constraints. However, for a recently proposed subclass of such methods that is built on the popular stochastic-gradient methodology from the unconstrained setting, convergence guarantees have been … Read more

A new upper bound of the Euclidean TSP constant

Categories Data Science Applications, Transportation Tags , ,

Let X1, X2, . . . , Xn be n independent and uniformly distributed random points in a compact region R ⊂ R2 of area 1. Let TSP(X1, . . . , Xn) denote the length of the optimal Euclidean traveling salesman tour that traverses all these points. The classical Beardwood-Halton-Hammersley theorem proves the existence … Read more

Mixed-Integer Quadratic Optimization and Iterative Clustering Techniques for Semi-Supervised Support Vector Machines

Categories (Mixed) Integer Nonlinear Programming, Data Science Algorithms, Data Science Applications Tags , , ,

Among the most famous algorithms for solving classification problems are support vector machines (SVMs), which find a separating hyperplane for a set of labeled data points. In some applications, however, labels are only available for a subset of points. Furthermore, this subset can be non-representative, e.g., due to self-selection in a survey. Semi-supervised SVMs tackle … Read more