Recently, the so-called $\psi$-learning approach, the Support Vector Machine (SVM) classifier obtained with the ramp loss, has attracted attention from the computational point of view. A Mixed Integer Nonlinear Programming (MINLP) formulation has been proposed for $\psi$-learning, but solving this MINLP formulation to optimality is only possible for datasets of small size. For datasets of … Read more
The structure of many real-world optimization problems includes minimization of a nonlinear (or quadratic) functional subject to bound and singly linear constraints (in the form of either equality or bilateral inequality) which are commonly called as continuous knapsack problems. Since there are efficient methods to solve large-scale bound constrained nonlinear programs, it is desirable to … Read more
In this paper we introduce the LeGO (Learning for Global Optimization) approach for global optimization in which machine learning is used to predict the outcome of a computationally expensive global optimization run, based upon a suitable training performed by standard runs of the same global optimization method. We propose to use a Support Vector Machine … Read more
In this work, we propose an inexact interior proximal type algorithm for solving convex second-order cone programs. This kind of problems consists of minimizing a convex function (possibly nonsmooth) over the intersection of an affine linear space with the Cartesian product of second-order cones. The proposed algorithm uses a distance variable metric, which is induced … Read more
We present a simple, first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and $\epsilon \in (0,1)$, the proposed algorithm computes a separating hyperplane whose margin is within a factor of $(1-\epsilon)$ of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended … Read more
In the interest of deriving classifiers that are robust to outlier observations, we present integer programming formulations of Vapnik’s support vector machine (SVM) with the ramp loss and hard margin loss. The ramp loss allows a maximum error of 2 for each training observation, while the hard margin loss calculates error by counting the number … Read more
Revenue management (RM) enhances the revenues of a company by means of demand-management decisions. An RM system must take into account the possibility that a booking may be canceled, or that a booked customer may fail to show up at the time of service (no-show). We review the Passenger Name Record data mining based cancellation … Read more
We consider a supervised classification problem in which the elements to be classified are sets with certain geometrical properties. In particular, this model can be applied to deal with data affected by some kind of noise and in the case of interval-valued data. Two classification rules, a fuzzy one and a crisp one, are defined … Read more
Linear support vector machine training can be represented as a large quadratic program. We present an efficient and numerically stable algorithm for this problem using interior point methods, which requires only O(n) operations per iteration. Through exploiting the separability of the Hessian, we provide a unified approach, from an optimization perspective, to 1-norm classification, 2-norm … Read more
We consider the problem of identifying multiple outliers in linear regression models. In robust regression the unusual observations should be removed from the sample in order to obtain better fitting for the rest of the observations. Based on the LTS estimate, we propose a penalized trimmed square estimator PTS, where penalty costs for discarding outliers … Read more