Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods

Ngueveu, Sandra Ulrich

doi:10.1016/j.ejor.2018.11.021

Cited by 13 publications

(9 citation statements)

References 18 publications

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“…Heuristics and exact methods exist to approximate univariate nonlinear functions (D ⊂ R) (Codsi et al [2021], Ngueveu [2019], Rebennack and Krasko [2020]). We are interested in bivariate functions (D ⊂ R 2 ) and to the best of our knowledge, only two papers address this case, with heuristics only:…”

Section: Problem Description and State Of The Artmentioning

confidence: 99%

Piecewise Linearization of Bivariate Nonlinear Functions: Minimizing the Number of Pieces Under a Bounded Approximation Error

Duguet

Ngueveu

2022

Lecture Notes in Computer Science

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This work focuses on the approximation of bivariate functions into piecewise linear ones with a minimal number of pieces and under a bounded approximation error. Applications include the approximation of mixed integer nonlinear optimization problems into mixed integer linear ones that are in general easier to solve. A framework to build dedicated linearization algorithms is introduced, and a comparison to the state of the art heuristics shows their efficiency. Piecewise linear approximation Bivariate nonlinear functions Mixed Integer Nonlinear Programming Heuristics

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Section: Problem Description and State Of The Artmentioning

confidence: 99%

Piecewise Linearization of Bivariate Nonlinear Functions: Minimizing the Number of Pieces Under a Bounded Approximation Error

Duguet

Ngueveu

2022

Lecture Notes in Computer Science

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“…Let f : ra, bs Ñ R be a function defined on a compact interval ra, bs Ď R. For the definition of piecewise linear approximation of f , we follow the notation in [58].…”

Section: Appendix C ∆-Approximation Of a Continuous Functionmentioning

confidence: 99%

Optimal Insurance under Maxmin Expected Utility

Birghila¹,

Boonen²,

Ghossoub³

2020

Preprint

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We examine a problem of demand for insurance indemnification, when the insured is sensitive to ambiguity and behaves according to the Maxmin-Expected Utility model of Gilboa and Schmeidler [43], whereas the insurer is a (risk-averse or risk-neutral) Expected-Utility maximizer. We characterize optimal indemnity functions both with and without the customary ex ante no-sabotage requirement on feasible indemnities, and for both concave and linear utility functions for the two agents. This allows us to provide a unifying framework in which we examine the effects of the no-sabotage condition, marginal utility of wealth, belief heterogeneity, as well as ambiguity (multiplicity of priors) on the structure of optimal indemnity functions. In particular, we show how the singularity in beliefs leads to an optimal indemnity function that involves full insurance on an event to which the insurer assigns zero probability, while the decision maker assigns a positive probability. We examine several illustrative examples, and we provide numerical studies for the case of a Wasserstein and a Rényi ambiguity set.

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“…Polynomial approximation methods have been considered by several studies in the literature [10][11][12][13][14][15][16][17][18][19][20][21][22]. In Ref.…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of an Error‐Margin Aware Approach for Non‐Uniform Segmentation of Elementary Functions Using Degree‐N Polynomial Approximation

Tahir,

Boudraa,

Lamini

et al. 2023

IEEJ Transactions Elec Engng

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Elementary functions are widely integrated in many embedded applications such as speech recognition and signal processing. This paper deals with the issues related to the hardware implementation of those functions. Indeed, a novel efficient Error‐Margin aware Approach for non‐uniform Segmentation of Elementary Functions using degree‐N Polynomial Approximation (EMASEF‐NPA) has been proposed. The bit‐width optimization (BWO) process has been used to obtain a better representation of the approximation polynomial coefficients. The principle of content‐addressable memory (CAM) and Horner's rules have been used in the physical implementation. Functional verification, logical synthesis, and physical implementation were performed using the FPGA platform. The results obtained using EMASEF‐NPA approach show a significant reduction, up to 70%, in the number of segments compared to conventional approaches. The findings of the physical implementation show a considerable decrease in area and delay. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.

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Piecewise linear bounding of univariate nonlinear functions and resulting mixed integer linear programming-based solution methods

Cited by 13 publications

References 18 publications

Piecewise Linearization of Bivariate Nonlinear Functions: Minimizing the Number of Pieces Under a Bounded Approximation Error

Piecewise Linearization of Bivariate Nonlinear Functions: Minimizing the Number of Pieces Under a Bounded Approximation Error

Optimal Insurance under Maxmin Expected Utility

Design and Implementation of an Error‐Margin Aware Approach for Non‐Uniform Segmentation of Elementary Functions Using Degree‐N Polynomial Approximation

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