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26th International Static Analysis Symposium (SAS)

作者： Yu, Hang Monniaux, David Univ Grenoble Alpes Grenoble INP CNRS F-38000 Grenoble France

ISBN: (纸本)9783030323042;9783030323035

Polyhedral projection is a main operation of the polyhedron abstract domain. It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method. In prior work, PLP was done in arbitrary precision rational arithmetic. In this paper, we present an approach where most of the computation is performed in floating-point arithmetic, then exact rational results are reconstructed. We also propose a workaround for a difficulty that plagued previous attempts at using PLP for computations on polyhedra: in general the linear programming problems are degenerate, resulting in redundant computations and geometric descriptions.

关键词： Polyhedral projection parametric linear programming Floating-point arithmetic

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Exact solution to a parametric linear programming problem

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NUMERICAL ALGORITHMS 2018年第4期78卷 1183-1194页

作者： Kolev, Lubomir Skalna, Iwona Tech Univ Sofia Sofia 1000 Bulgaria AGH Univ Sci & Technol Aleja Adama Mickiewicza 30 PL-30059 Krakow Poland

We consider the problem of determining the interval hull solution l (au) to a parametric linear programming (PLP) problem l(x, p) = c (T) (p)x, where c (i) (p) can be in general nonlinear functions of p, and x satisfy the constraint A(p)x = b(p), p a p. A new iterative method for determining l (au) is suggested. The method exploits the concept of the p-solution to a square linear interval parametric (LIP) system, having the parametric form x(p) = L p + a, p a p, where L is a real n x m matrix (n and m are, respectively, the sizes of the square matrix A and vector p), whereas a is an interval vector. A numerical example is provided to illustrate the new approach.

关键词： p-solution linear interval parametric system parametric linear programming Interval hull solution

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Scalable Minimizing-Operators on Polyhedra via parametric linear programming 1

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24th International Static Analysis Symposium (SAS)

作者： Marechal, Alexandre Monniaux, David Perin, Michael Univ Grenoble Alpes CNRS VERIMAG F-38000 Grenoble France

ISBN: (数字)9783319667065

ISBN: (纸本)9783319667065;9783319667058

Convex polyhedra capture linear relations between variables. They are used in static analysis and optimizing compilation. Their high expressiveness is however barely used in verification because of their cost, often prohibitive as the number of variables involved increases. Our goal in this article is to lower this cost. Whatever the chosen representation of polyhedra - as constraints, as generators or as both - expensive operations are unavoidable. That cost is mostly due to four operations: conversion between representations, based on Chernikova's algorithm, for libraries in double description;convex hull, projection and minimization, in the constraints-only representation of polyhedra. Libraries operating over generators incur exponential costs on cases common in program analysis. In the Verimag Polyhedra Library this cost was avoided by a constraints-only representation and reducing all operations to variable projection, classically done by Fourier-Motzkin elimination. Since Fourier-Motzkin generates many redundant constraints, minimization was however very expensive. In this article, we avoid this pitfall by expressing projection as a parametric linear programming problem. This dramatically improves efficiency, mainly because it avoids the post-processing minimization. We show how our new approach can be up to orders of magnitude faster than the previous approach implemented in the Verimag Polyhedra Library that uses only constraints and Fourier-Motzkin elimination, and on par with the conventional double description approach, as implemented in well-known libraries.

关键词： Polyhedra parametric linear programming Projection

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Optimal bidding strategy for GENCOs based on parametric linear programming considering incomplete information

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2015年第Mar.期66卷 272-279页

作者： Gao, Feng Sheble, Gerald B. Hedman, Kory W. Yu, Chien-Ning SGRI North Amer Santa Clara CA 95054 USA Iowa State Univ Ames IA 50011 USA Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ USA Ventyx Santa Clara CA 95050 USA

Electric energy market participants face risks and uncertainties associated with the ever-changing market environment. A profit-driven bidding decision tool is thus crucial for generation companies (GENCOs) to maintain a competitive position. Although optimal bidding strategies have been extensively studied in the literature, most previous research assumes continuous and differentiable generation offer curves, whereas actual offer curves are piecewise staircase curves. Based on the foregoing, this paper presents an optimal bidding strategy for GENCOs, derived by using parametric linear programming, and extends the proposed method to consider incomplete information. We show that the proposed algorithm is able to utilize the characteristics of piecewise staircase energy offer curves in contrast to the findings of previous researchers. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Bidding strategy Decision analysis Incomplete information parametric linear programming Non-convex optimization

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Performance analysis of sustainable development goals: a multi-component additive network DEA approach

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2024年

作者： Keskin, Burak Zhu, Joe Yu, Anyu Cankiri Karatekin Univ Uluyazi Campus Fac Econ & Adm Sci Cankiri Turkiye Worcester Polytech Inst Worcester MA USA Zhejiang Gongshang Univ Hangzhou Peoples R China

The Sustainable Development Goals (SDGs) were created under 17 important headings announced by the United Nations (UN) in 2015. Three interconnected principles of sustainable development - Social, Environmental, and Economic- form the fundamental pillars of SDGs. No study has attempted to measure SDGs performances of countries in a single network model using these basic dimensions. To fill this gap, this study uses three-stage additive network Data Envelopment Analysis (DEA) to monitor the performance of 29 Organisation for Economic Co-operation and Development (OECD) countries from 2015 to 2018. Our analysis reveals that the performance of OECD member countries in the environmental balance division is much lower than in the social progress and socio-economic divisions. Each country should identify its weaknesses in specific divisions and allocate more effort accordingly. We find none of the countries are overall efficient but a few are efficient in one or two divisions such as Latvia, Norway, Ireland, Slovenia, Finland, and USA. Based on the findings we recommend that the OECD countries should primarily focus on environmental issues to promote their overall performance in achieving SDGs. Our results underscore the notion that economic strength does not invariably equate to the achievement of SDGs as well.

关键词： Sustainable development goals data envelopment analysis additive network DEA parametric linear programming

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Dynamic hedging in incomplete markets using risk measures

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IMA JOURNAL OF MANAGEMENT MATHEMATICS 2022年第2期33卷 345-367页

作者： Gaillardetz, Patrice Hachem, Saeb Concordia Univ Dept Math & Stat Montreal PQ H3G 1M8 Canada

In this paper, we consider the pricing of financial derivatives that involve dynamic hedging strategies and payments within the planning horizon. Equity-indexed annuities (EIAs), guaranteed investment certificates (GICs) and American and barrier options are typical examples of these products. Our exploration involves the use and comparison of alternative models that use risk measures. Although the hedging is done for each observation of the input stochastic process, the appropriate mix of risk measures and state dynamic equations helps the issuer to appropriately tailor the overall risk exercise. These different models are solved by a unified backward stochastic dynamic programming framework that we imbed with parametric techniques to shorten the running time and manage the curse of dimensionality in dynamic programming. To demonstrate the flexibility of this framework we present numerical examples featuring GICs and point-to-point EIAs. Finally, by using sampling techniques, optimal hedging strategies and specific indicators of the hedging performance, we make recommendations on how to fine tune the risk measure parameters.

关键词： partial hedging local risk-minimizing strategies stochastic dynamic programming linear programming parametric linear programming risk measures

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The role of livestock feed fertilization as an improvement of sustainability in the dairy sector

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SUSTAINABLE PRODUCTION AND CONSUMPTION 2022年 31卷 448-458页

作者： Quintero-Herrera, Samuel Zwolinski, Peggy Evrard, Damien CanoGmez, Jos Julin Botello-Alvarez, Jos Enrique Rivas-Garca, Pasiano Univ Autonoma Nuevo Leon Fac Ciencias Quim Dept Ingn Quim Ave Univ S-NCd Univ San Nicolas De Los Garza 64451 Nuevo Leon Mexico Univ Autonoma Nuevo Leon Fac Ciencias Quim Ctr Invest Biotecnol & Nanotecnol Parque Invest Innovac Tecnol km 10 Highway Int Airport Mariano Escobedo Apodaca 66629 Nuevo Leon Mexico Univ Grenoble Alpes CNRS Grenoble INP G SCOP 38000 Grenoble France Inst Tecnol Celaya Dept Ingn Bioquim Ave Tecnol & A Garcia Cubas Guanajuato 38010 Mexico

Fertilization of crops used as feed in the dairy industry represents up to 50% of greenhouse gases (GHG) and 30% of milk production costs. The environmental impacts raised from this activity are mainly associated with fertilizer manufacturing. Proper fertilizer selection for feed production is an alternative to improve the dairy industry's sustainability. This study proposes a strategy to mitigate the environmental and economic impacts in the dairy industry via optimization of crop fertilizer blends by using a parametric linear programming model. Individual fertilizers' environmental impacts and costs were evaluated through the ecoinvent database v. 3.3. and govern-mental information, respectively. The effect of the optimized fertilizer blends used in each crop on the life cycle of a dairy supply chain in the Mexican Bajio region was evaluated. Three analysis tiers were considered: livestock feed production, dairy cattle diet, and dairy farming system. The optimization results of fertilizer blends revealed an opposite behavior between the environmental and cost indicators for all crops;a reduction of 1% in the environmental impacts could increase the fertilization cost by 5.5%. In addition, the results indicated that with the use of optimized fertilizer blends, a reduction of GHG emissions up to 22 g CO2 eq kg(-1)& nbsp;of milk could be achieved compared with those conventional ones. Focused on the Mexican Bajio region, this contribution implies up to 2.2% of Mexico's commitments in the COP21 agreement for the livestock sector. Our results show that potential savings in costs of 29.6 MUSD y(-1) could be reached when the most economical fertilizer blends are used in the optimization. This work presents an alternative to improve the sustainability in the dairy sector, which could be easily implemented for the agricultural producers, especially in countries such as Mexico, where government budgets dedicated to mitigating environmental impacts are limited. (C)& nbsp;202

关键词： Dairy industry Fertilizer blends Life cycle assessment parametric linear programming Optimization

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Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2021年第2期291卷 491-496页

作者： De Wolf, Daniel Smeers, Yves Univ Littoral Cote dOpale TVES EA 4477 220 Ave Univ F-59140 Dunkerque France Catholic Univ Louvain CORE Voie Roman Pays 34 B-1348 Louvain La Neuve Belgium

We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/)

关键词： linear programming parametric linear programming Nondifferentiable programming

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A New Non-Iterative Method for Collaborative Optimization Model Considering Coordination of Active Distribution Network and Multi Agents

A New Non-Iterative Method for Collaborative Optimization Mo...

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Power System and Green Energy Conference (PSGEC)

作者： Liu, Yang Li, Lisheng Zheng, Zhong Li, Mingyang Liu, Hejing Miao, Shihong State Grid Shandong Elect Power Res Inst Equipment Condit Evaluat Ctr Jinan Peoples R China Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan Peoples R China Univ Manchester Sch Elect Engn Manchester Lancs England

ISBN: (纸本)9781728190952

Active distribution network is one of the important means to promote the safe consumption of clean energy and realize the sustainable development of power grid in the future. This paper presents a new non-iterative method for collaborative optimization model considering coordination of active distribution network and multi agents. Firstly, taking the technical economy of active distribution network as the objective, the optimization model of active distribution network is established, and the second-order cone relaxation is used to realize the non-convex constraint transformation of the model. Secondly, the optimization model of agent is established with the goal of the lowest total energy consumption cost, and then a three-layer optimization architecture of multi agents is proposed. Thirdly, fully considering the active distribution network and multi-agent information energy interaction, a non iterative collaborative optimization method based on the theory of parametric linear programming is proposed. Finally, the effectiveness of the model and algorithm proposed in this paper is verified through example analysis.

关键词： Non-iterative Collaborative optimization model Active distribution network Multi agents Second-order cone relaxation parametric linear programming

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Identification of Minimum Set of Master Regulatory Genes in Gene Regulatory Networks

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IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020年第3期17卷 999-1009页

作者： Bakhteh, Somayeh Ghaffari-Hadigheh, Alireza Chaparzadeh, Nader Azarbaijan Shahid Madani Univ Tabriz 53714161 East Azerbaijan Iran

Identification of master regulatory genes is one of the primary challenges in systems biology. The minimum dominating set problem is a powerful paradigm in analyzing such complex networks. In these models, genes stand as nodes and their interactions are assumed as edges. Here, members of a minimal dominating set could be regarded as master genes. As finitely many minimum dominating sets may exist in a network, it is difficult to identify which one represents the most appropriate set of master genes. In this paper, we develop a weighted gene regulatory network problem with two objectives as a version of the dominating set problem. Collective influence of each gene is considered as its weight. The first objective aims to find a master regulatory genes set with minimum cardinality, and the second objective identifies the one with maximum weight. The model is converted to a single objective using a parameter varying between zero and one. The model is implemented on three human networks, and the results are reported and compared with the existing model of weighted network. parametric programming in linear optimization and logistic regression are also implemented on the arisen relaxed problem to provide a deeper understanding of the results. Learned from computational results in parametric analysis, for some ranges of priorities in objectives, the identified master regulatory genes are invariant, while some of them are identified for all priorities. This would be an indication that such genes have higher degree of being master regulatory ones, specially on the noisy networks.

关键词： Optimization Mathematical model Proteins Biological system modeling programming linear programming Master gene gene regulatory network minimum dominating set bi-objective optimization parametric linear programming

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