Dominating Sets for Convex Functions with some Applications

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity. In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems. The applicability of the results obtained is illustrated with the statement of new localization results in the fields of Linear Regression and Location

Dominating Sets for Convex Functions with some Applications

A number of optimization methods require as a first step the construction of a dominating set (a set containing an optimal solution) enjoying properties such as compactness or convexity.In this note we address the problem of constructing dominating sets for problems whose objective is a componentwise nondecreasing function of (possibly an infinite number of) convex functions, and we show how to obtain a convex dominating set in terms of dominating sets of simpler problems.The applicability of the results obtained is illustrated with the statement of new localization results in the fields of Linear Regression and Location.location;convexity;regression;dominating set

An optimization tool to design the field of a Solar Power Tower plant allowing heliostats of different sizes

The design of a Solar Power Tower plant involves the optimization of the heliostat field layout. Fields are usually designed to have all heliostats of identical size. Although the use of a single heliostat size has been questioned in the literature, there are no tools to design fields with heliostats of several sizes at the same time. In this paper, the problem of optimizing the heliostat field layout of a system with heliostats of different sizes is addressed. We present an optimization tool to design solar plants allowing two heliostat sizes. The methodology is illustrated with a particular example considering different heliostat costs.MTM2013-41286-P (Spain) MTM2015-65915-R (Spain) P11-FQM-7603 (Andalucía) TD1207 (EU COST Action

Functional-bandwidth kernel for Support Vector Machine with Functional Data:An alternating optimization algorithm

Functional Data Analysis (FDA) is devoted to the study of data which are functions. Support Vector Ma- chine (SVM) is a benchmark tool for classification, in particular, of functional data. SVM is frequently used with a kernel (e.g.: Gaussian) which involves a scalar bandwidth parameter. In this paper, we pro- pose to use kernels with functional bandwidths. In this way, accuracy may be improved, and the time intervals critical for classification are identified. Tuning the functional parameters of the new kernel is a challenging task expressed as a continuous optimization problem, solved by means of a heuristic. Our experiments with benchmark data sets show the advantages of using functional parameters and the ef- fectiveness of our approach

Variable selection in classification for multivariate functional data

When classification methods are applied to high-dimensional data, selecting a subset of the predictors may lead to an improvement in the predictive ability of the estimated model, in addition to reducing the model complexity. In Functional Data Analysis (FDA), i.e., when data are functions, selecting a subset of predictors corresponds to selecting a subset of individual time instants in the time interval in which the functional data are measured. In this paper, we address the problem of selecting the most informative time instants in multivariate functional data, a case much less studied than its single-variate counterpart. Our proposal allows one to use in a very simple way high-order information of the data, e.g. monotonicity or convexity by means of the functional data derivatives. The aforementioned problem is addressed with tools of Global Optimization in continuous variables: the time instants are selected to maximize the correlation between the class label and the Support Vector Machine score used for classification. The effectiveness of the proposal is shown in univariate and multivariate datasets

On the selection of the globally optimal prototype subset for nearest-neighbor classification

The nearest-neighbor classifier has been shown to be a powerful tool for multiclass classification. We explore both theoretical properties and empirical behavior of a variant method, in which the nearest-neighbor rule is applied to a reduced set of prototypes. This set is selected a priori by fixing its cardinality and minimizing the empirical misclassification cost. In this way we alleviate the two serious drawbacks of the nearest-neighbor method: high storage requirements and time-consuming queries. Finding this reduced set is shown to be NP-hard. We provide mixed integer programming (MIP) formulations, which are theoretically compared and solved by a standard MIP solver for small problem instances. We show that the classifiers derived from these formulations are comparable to benchmark procedures. We solve large problem instances by a metaheuristic that yields good classification rules in reasonable time. Additional experiments indicate that prototype-based nearest-neighbor classifiers remain quite stable in the presence of missing values

Energy efficiency in the mineral resources and raw materials complex

Energy efficiency and energy saving at all times and especially at the present stage of development of industry and economy have played an extremely important role. Regardless of which countries and according to what criteria they build energy development plans, energy efficiency and energy saving are always a priority. This fully applies to the mineral resources complex, in which energy consumption as a whole makes up a large share of total consumption. The resources mined in the mineral resources complex are themselves a source of energy. The energy sector is evolving in many ways. Many scientific works, the results of which are reflected in publications, confirm the relevance of research in the energy efficiency field. But the approach to individual decisions in the mineral resource industry is specific and it is worth of separate consideration. Recently, much attention has been paid to “green energy” and renewable energy sources. However, energy efficiency in the field of traditional generation and consumption remains an urgent problem and its solution is in constant development. One of the main directions for improving energy efficiency is the development of autonomous systems for the electrical and thermal power engineering. All these problems are reflected in a special volume of the Journal of the Mining Institute, the articles are divided into four sections: energy efficiency of the electric drive in the mineral resources complex (MRC); energy efficiency of industrial plants and enterprises in MRC; power quality and renewable sources in MRC; autonomous power supply systems in MRC. The presented articles contain valuable material from the scientific and practical points of view and can form the basis for further research in the energy efficiency field

Maximizing upgrading and downgrading margins for ordinal regression

In ordinal regression, a score function and threshold values are sought to classify a set of objects into a set of ranked classes. Classifying an individual in a class with higher (respectively lower) rank than its actual rank is called an upgrading (respectively downgrading) error. Since upgrading and downgrading errors may not have the same importance, they should be considered as two different criteria to be taken into account when measuring the quality of a classifier. In Support Vector Machines, margin maximization is used as an effective and computationally tractable surrogate of the minimization of misclassification errors. As an extension, we consider in this paper the maximization of upgrading and downgrading margins as a surrogate of the minimization of upgrading and downgrading errors, and we address the biobjective problem of finding a classifier maximizing simultaneously the two margins. The whole set of Pareto-optimal solutions of such biobjective problem is described as translations of the optimal solutions of a scalar optimization problem. For the most popular case in which the Euclidean norm is considered, the scalar problem has a unique solution, yielding that all the Pareto-optimal solutions of the biobjective problem are translations of each other. Hence, the Pareto-optimal solutions can easily be provided to the analyst, who, after inspection of the misclassification errors caused, should choose in a later stage the most convenient classifier. The consequence of this analysis is that it provides a theoretical foundation for a popular strategy among practitioners, based on the so-called ROC curve, which is shown here to equal the set of Pareto-optimal solutions of maximizing simultaneously the downgrading and upgrading margins

Short communication: An association analysis between one missense polymorphism at the SREBF1 gene and milk yield and composition traits in goats

Sterol regulatory element binding transcription factor 1 (SREBF1) regulates the expression of genes involved in the biosynthesis of fatty acids and cholesterol. Herewith, we have sequenced the near-complete coding region and part of the 3?UTR of the goat SREBF1 gene. In doing so, we have detected a missense c.353CT polymorphism causing a proline to leucine substitution at position 118 (P118L). An association analysis with milk composition traits recorded in MurcianoGranadina goats only revealed a statistical tendency linking SREBF1 genotype and milk omega-3 fatty acid content. The lack of significant associations suggests that the P118L substitution does not involve a functional change.Le facteur de transcription de´nomme´ Sterol regulatory element binding transcription factor 1 (SREBF1) re´gule l’expression des ge`nes implique´s dans la biosynthe`se des acides gras et du choleste´rol. Dans cette e´tude, nous avons se´quence´ la quasi-totalite´ de la re´gion codante et une partie du la re´gion 3?UTR du ge`ne SREBF1 de la che`vre. Ce travail, nous a permis d’identifier un polymorphisme non-synonyme c.353CT causant la substitution d’une Proline en Leucine a` la position 118. L’e´tude d’association avec la composition du lait enregistre´e en che`vres Murciano-Granadina, a re´ve´le´ seulement une tendance statistique reliant SREBF1 ge´notype et l’acide gras ome´ga-3 du lait. L’absence d’associations significatives sugge`re que la substitution P118L n’implique pas un changement fonctionnel