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EUROPEAN JOURNAL OF CONTROL 2003年第2-3期9卷 177-189页

作者： Morari, M Baotic, M Borrelli, F ETH Zentrum Automat Control Lab CH-8092 Zurich Switzerland

Piece-wise affine and mixed logical dynamical models for discrete time linear hybrid systems are reviewed. Constrained optimal control problems with linear and quadratic objective functions are defined. Some results on the structure and computation of the optimal control laws are presented. The effectiveness of the techniques is illustrated on a wide range of practical applications.

关键词： hybrid systems mixed-integer programming optimal control parametric programming switched systems

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A minimax resource allocation problem with variable resources

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第1期136卷 46-56页

作者： Gol'stejn, EG Dempe, S Freiberg Univ Min & Technol Inst Angew Math 2 TU Bergakad Freiberg D-09596 Freiberg Germany Russian Acad Sci Moscow 117418 Russia

The problem of optimally allocating the resources to competing activities where the amounts of the resources are not only previosly given but are also to be determined subject to certain linear constraints is considered. The objective is to find such activity levels such that their weighted deviation from a prespecified target is as small as possible. A primal decomposition approach for the problem and derive an explicit formula for the piecewise affine-linear convex objective function of the upper level problem are suggested. The lower level problem is a parametric optimization problem with a bottleneck objective function. If the constraints on the amounts of the resources are all of knapsack type or if there is only one such constraint, then the upper level problem is equivalent to the lower level problem with fixed right-hand sides. In the general case, the problem can efficiently be solved by means of the level method. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： convex programming parametric programming minimax resource allocation

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NECESSARY OPTIMALITY CONDITIONS FOR STACKELBERG PROBLEMS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1993年第2期76卷 305-320页

作者： OUTRATA, JV 1. Institute of Information Theory and Automation Prague Czechoslovakia

First-order necessary optimality conditions are derived for a class of two-level Stackelberg problems in which the followers' lower-level problems are convex programs with unique solutions. To this purpose, generalized Jacobians of the marginal maps corresponding to followers' problems are estimated. As illustrative examples, two discretized optimum design problems with elliptic variational inequalities are investigated. The theoretical results may be used also for the numerical solution of the Stackelberg problems considered by nondifferentiable optimization methods.

关键词： STACKELBERG PROBLEMS GENERALIZED JACOBIANS parametric programming

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A membership function approach for aggregate production planning problems in fuzzy environments

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2010年第23期48卷 7003-7023页

作者： Chen, Shih-Pin Huang, Wen-Lung Natl Chung Cheng Univ Dept Business Adm Chiayi 621 Taiwan

This paper proposes a novel approach for the aggregate production planning (APP) problem with fuzzy parameters. Different from the results of previous studies, in this paper the membership function of the fuzzy minimal total cost is constructed based on Zadeh's extension principle and fuzzy solutions are provided. A pair of mathematical programs parameterised by possibility level is formulated to calculate the lower and upper bounds of the fuzzy total cost at . By enumerating different values of , the membership function of the fuzzy total cost is constructed. To illustrate the validity of the proposed approach, the example studied by Lai and Hwang (1992) using Chanas's approach is investigated. Since the objective value is expressed by a membership function rather than by a crisp value, the proposed approach can represent APP systems more accurately, thus obtained solutions which contain more information can offer more chance to achieve the feasible disaggregate plan, and it is beneficial to the decision-maker in practical applications. The proposed approach can also be applied to APP problems with other characteristics.

关键词： aggregate production planning fuzzy sets membership function non-linear programming parametric programming

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parametric process synthesis for general nonlinear models

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COMPUTERS & CHEMICAL ENGINEERING 2003年第10期27卷 1499-1512页

作者： Banerjee, I Ierapetritou, MG Rutgers State Univ Dept Chem & Biochem Engn Piscataway NJ 08854 USA

This paper presents a new approach towards parametric analysis of MINLP models in the context of process synthesis problems under uncertainty. The approach is based on the idea of High Dimensional Model Representation technique which utilize a reduced number of model runs to build an uncertainty propagation model that expresses the variability of optimal solution in the uncertain space. Based on this idea, a systematic procedure is developed where in the first step the possible changes in the optimal design configurations due to parametric uncertainty are identified. In the next step, the variability of optimal solution with parameter uncertainty for each design is captured. Having obtained a parametric expression of optimal objective for each design, the optimal solution can be determined by comparing the solutions for different designs. The proposed approach provides information about variation of the optimal objective and optimal design configuration over the entire uncertain space. This information can then be judiciously utilized in any decision making depending on specific process requirements. The main advantage of the proposed approach is that it does not depend on the nature or existence of a mathematical model to describe the input-output relationship of the process. (C) 2003 Elsevier Science Ltd. All rights reserved.

关键词： parametric programming process synthesis HDMR

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LOCAL STABILITY OF SOLUTIONS TO DIFFERENTIABLE OPTIMIZATION PROBLEMS IN BANACH-SPACES

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1991年第3期70卷 443-466页

作者： ALT, W 1. Mathematisches Institut Universit?t Bayreuth Bayreuth Germany

This paper considers a class of nonlinear differentiable optimization problems depending on a parameter. We show that, if constraint regularity, a second-order sufficient optimality condition, and a stability condition for the Lagrange multipliers hold, then for sufficiently smooth perturbations of the constraints and the objective function the optimal solutions locally obey a type of Lipschitz condition. The results are applied to finite-dimensional problems, equality constrained problems, and optimal control problems.

关键词： NONLINEAR OPTIMIZATION parametric programming STABILITY OF SOLUTIONS OPTIMAL CONTROL

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Coordinated Heat and Power Dispatch Considering Mutual Benefit and Mutual Trust: A Multi-party Perspective

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2022年第1期13卷 251-264页

作者： Chen, Binbin Wu, Wenchuan Sun, Hongbin Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Coordinated heat and power dispatch has attracted increasing attention due to its flexibility support for renewable energy accommodation. Different from most conventional studies that regard coordination as holistic optimization, in which power systems monopolize the additional payoff brought by coordination while heating systems suffer from higher heat supply costs, this work considers coordinated dispatch from a novel multi-party perspective to ensure the privacy protection, mutual benefit, and mutual trust of all participants. Based on the existing works that address the privacy issue well, we propose a transfer payment strategy to ensure that both heating systems and power systems benefit from coordinated dispatch. The calculation of transfer payments is performed through a parametric programming method, which discloses only the payoff variation and maintains the privacy of the payoff itself. Finally, a critical region tracking method is developed to confirm the authenticity of the information exchanged between power systems and heating systems, which prevents possible defrauding. Numerical tests indicate that our proposed approach achieves the mutual benefit of both systems in coordinated dispatch and detects inauthentic information effectively to ensure mutual trust.

关键词： Heating systems Power systems Cogeneration Privacy Resistance heating Schedules programming Combined heat and power economic dispatch mutual benefit mutual trust parametric programming transfer payment

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A NEW FAULT TREE ANALYSIS METHOD: FUZZY DYNAMIC FAULT TREE ANALYSIS

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EKSPLOATACJA I NIEZAWODNOSC-MAINTENANCE AND RELIABILITY 2012年第3期14卷 208-214页

作者： Li, Yan-Feng Huang, Hong-Zhong Liu, Yu Xiao, Ningcong Li, Haiqing Univ Elect Sci & Technol China Sch Mech Elect & Ind Engn Chengdu 611731 Sichuan Peoples R China

Fault tree analysis (FTA) is a widely used reliability assessment tool for large and complex engineering systems. The conventional fault tree analysis method, which contains AND, OR, and Voting gates, etc., can efficiently build an analytical model to represent combinations of component failures that cause the failure of a system. However, due to its limited modeling capability, we may confront difficulties when modeling dynamic systems which involve complicated dynamic characteristics such as sequence dependency and functional dependency. Markov-based dynamic fault tree analysis (DFTA) extends the static FTA by introducing additional gates to model such complicated interactions among events. In many circumstances, it is quite difficult to obtain an accurate system reliability estimate due to limited data. To overcome this issue, a fuzzy dynamic fault tree model is put forth to assess system reliability. To obtain the membership function of the fuzzy probability for the top event of the studied fault trees, the extension principle is employed to calculate the associated membership function via a pair of parametric programming problems. Finally, a case study is presented to demonstrate the application of the proposed approach for the hydraulic system of a CNC machining centre.

关键词： Fault tree analysis Dynamic fault tree Fuzzy number Fuzzy Markov model parametric programming

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Cost efficiency measurement with fuzzy data in DEA

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017年第1期32卷 409-420页

作者： Aghayi, Nazila Islamic Azad Univ Dept Math Ardabil Branch Ardebil Iran

Being a nonparametric method, data envelopment analysis (DEA) is confined to measuring the efficiency of a collection of decision making units (DMUs) consuming multiple crisp inputs to produce multiple crisp outputs. Since not all data in the real world have determined values, and input and output values for DMUs are often subject to fluctuation, the concept of fuzziness has been introduced to deal with such imprecise data. This study intends to evaluate the cost efficiency of DMUs in three different scenarios, with one distinct model proposed for each scenario. The main idea is to use the alpha-cut method and the extension principle to convert the fuzzy cost efficiency model into a family of conventional crisp DEA models by obtaining one lower bound and one upper bound for the cost efficiency score of a DMU for any alpha varying between 0 and 1. When the lower and upper bounds are invertible with respect to alpha, the membership function of the fuzzy efficiency of a DMU-which falls within the scope of parametric programming problems-can be obtained by finding the inverse of the lower and upper bounds as well as employing the extension principle. In this case, the value of fuzzy cost efficiency varies between 0 and 1. Otherwise, the cost efficiency scores of DMUs can be specified as intervals, which are actually alpha-cuts of the fuzzy membership function, by collecting results for different alpha values. Furthermore, we demonstrate that Farrell's decomposition also holds for cost efficiency with fuzzy data. In addition, all DMUs are divided into three classes in each scenario, with cost-efficient and cost-inefficient DMUs falling into independent classes. In other words, units which are cost-inefficient in the upper bound for any alpha ranging between 0 and 1 will definitely be cost-inefficient in the lower bound, too, and the units will be cost-efficient in the upper bound if they are cost-efficient in the lower bound for a specific alpha varying between 0 and 1.

关键词： Data envelopment analysis cost efficiency membership function parametric programming alpha-cut fuzzy

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ON THE OPTIMAL VALUE FUNCTION FOR CERTAIN LINEAR-PROGRAMS WITH UNBOUNDED OPTIMAL SOLUTION SETS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1985年第1期46卷 55-66页

作者： BENSON, HP 1.Department of Management and Administrative Sciences College of Business Administration University of Florida Gainesville Florida

Often, the coefficients of a linear programming problem represent estimates of true values of data or are subject to systematic variations. In such cases, it is useful to perturb the original data and to either compute, estimate, or otherwise describe the values of the functionf which gives the optimal value of the linear program for each perturbation. If the right-hand derivative off at a chosen point exists and is calculated, then the values off in a neighborhood of that point can be estimated. However, if the optimal solution set of either the primal problem or the dual problem is unbounded, then this derivative may not exist. In this note, we show that, frequently, even if the primal problem or the dual problem has an unbounded optimal solution set, the nature of the values off at points near a given point can be investigated. To illustrate the potential utility of our results, their application to two types of problems is also explained.

关键词： Optimal value function linear programming sensitivity analysis parametric programming multiple-objective linear programming

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