Piecewise linear function

About: Piecewise linear function is a research topic. Over the lifetime, 8133 publications have been published within this topic receiving 161444 citations.

A multiplicative model for efficiency analysis

Abstract: This paper develops theory and algorithms for a “multiplicative” Data Envelopment Analysis (DEA) model employing virtual outputs and inputs as does the CCR ratio method for efficiency analysis. The frontier production function results here are of piecewise log-linear rather than piecewise linear form.

Techniques for non-linear magnification transformations

Abstract: This paper presents efficient methods for implementing general non-linear magnification transformations. Techniques are provided for: combining linear and non-linear magnifications, constraining the domain of magnifications, combining multiple transformations, and smoothly interpolating between magnified and normal views. In addition, piecewise linear methods are introduced which allow greater efficiency and expressiveness than their continuous counterparts.

A Mixed-Integer Linear Programming Approach for Multi-Stage Security-Constrained Transmission Expansion Planning

Abstract: The transmission expansion planning (TEP) problem in modern power systems is a large-scale, mixed-integer, non-linear and non-convex problem. Although remarkable advances have been made in optimization techniques, finding an optimal solution to a problem of this nature can still be extremely challenging. Based on the linearized power flow model, this paper presents a mixed-integer linear programming (MILP) approach that considers losses, generator costs and the N - 1 security constraints for the multi-stage TEP problem. The losses and generator cost are modeled as piecewise linear functions of the line flows and the generator outputs, respectively. The IEEE 24-bus system is used to compare the lossy and the lossless model. The results show that the lossy model provides savings in total cost in the long run. The selection of the best number of piecewise linear sections L is also shown. Then a complete planning framework is presented and a multi-stage TEP is performed on the IEEE 118-bus test system. Simulation results show that the proposed approach is accurate and efficient, and has the potential to be applied to large-scale power system planning problems.

Nearest Neighbor Classification of Remote Sensing Images With the Maximal Margin Principle

Abstract: In this paper, we present a new variant of the k-nearest neighbor (kNN) classifier based on the maximal margin principle. The proposed method relies on classifying a given unlabeled sample by first finding its k-nearest training samples. A local partition of the input feature space is then carried out by means of local support vector machine (SVM) decision boundaries determined after training a multiclass SVM classifier on the considered k training samples. The labeling of the unknown sample is done by looking at the local decision region to which it belongs. The method is characterized by resulting global decision boundaries of the piecewise linear type. However, the entire process can be kernelized through the determination of the k -nearest training samples in the transformed feature space by using a distance function simply reformulated on the basis of the adopted kernel. To illustrate the performance of the proposed method, an experimental analysis on three different remote sensing datasets is reported and discussed.