Topic
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.
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TL;DR: In this paper, a nonlinear model predictive control (NMPC) based on a piecewise linear Wiener model is applied to a polymerization reactor as a MIMO process.
71 citations
TL;DR: Evaluation of the global approximate error provides efficient curve approximations, irrespective of shape complexity, number of sampled points, and irregularity of sampling interval.
71 citations
TL;DR: The proposed ramp-LPSVM is a piecewise linear minimization problem and the related optimization techniques are applicable, and the result is more robust than that of hinge SVMs and is sparser than the result of ramp-SVM, which consists of the || ċ || k-penalty and the ramp loss.
Abstract: The ramp loss is a robust but non-convex loss for classification. Compared with other non-convex losses, a local minimum of the ramp loss can be effectively found. The effectiveness of local search comes from the piecewise linearity of the ramp loss. Motivated by the fact that the l1-penalty is piecewise linear as well, the l1-penalty is applied for the ramp loss, resulting in a ramp loss linear programming support vector machine (ramp-LPSVM). The proposed ramp-LPSVM is a piecewise linear minimization problem and the related optimization techniques are applicable. Moreover, the l1-penalty can enhance the sparsity. In this paper, the corresponding misclassification error and convergence behavior are discussed. Generally, the ramp loss is a truncated hinge loss. Therefore ramp-LPSVM possesses some similar properties as hinge loss SVMs. A local minimization algorithm and a global search strategy are discussed. The good optimization capability of the proposed algorithms makes ramp-LPSVM perform well in numerical experiments: the result of ramp-LPSVM is more robust than that of hinge SVMs and is sparser than that of ramp-SVM, which consists of the || ċ || k-penalty and the ramp loss.
71 citations
TL;DR: In this paper, the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance was investigated and both the undamped and the damped DVAs were considered.
Abstract: This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many subharmonics appear. The damped DVA suppresses the first harmonic resonance as well as its super- and subharmonics.
71 citations
TL;DR: In this article, two domain partitions are proposed that give rise to region configurations practically meaningful for the realizability of lattice models, and discussed and connected with the domain partition generated by the set of boundaries, frequently considered when dealing with PWL functions.
70 citations