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Interactive stability of vector optimization problems

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2001年第3期134卷 616-622页

作者： Kassem, MA Tanta Univ Fac Sci Dept Math Tanta Egypt

This paper presents a solution method for multiobjective nonlinear programming (MONLP) problems and the stability of this solution. The method. called interactive stability compromise programming (ISCP), offers a practical solution to MONLP problems by deriving the compromise weights and combining judgement with an automatic optimization technique in fuzzy decision making. This is achieved by using the method of compromise programming and the method of compromise weights and we obtain the stability for the solution in each step of the algorithm. A numerical example illustrates various aspects of the results developed in this paper. (C) 2001 Published by Elsevier Science B.V.

关键词： MONLP stability interactive decision making compromise weights parametric programming membership functions

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Hybrid systems modeling and control

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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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SENSITIVITY ANALYSIS OF NONLINEAR PROGRAMS AND DIFFERENTIABILITY PROPERTIES OF METRIC PROJECTIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1988年第3期26卷 628-645页

作者： SHAPIRO, A Univ of South Africa South Africa

This paper is concerned with a study of differentiability properties of the optimal value function and an associated optimal solution of a parametrized nonlinear program. Second order analysis is presented essentially under the Mangasarian-Fromovitz constraint qualification when the corresponding vector of Lagrange multipliers is not necessarily unique. It is shown that under certain regularity conditions the optimal value function possesses second order directional derivatives and the optimal solution mapping is directionally differentiable. The results obtained are applied to an investigation of metric projections in finite-dimensional spaces.

关键词： 90C31 nonlinear programming sensitivity analysis optimal value parametric programming metric projections second order directional derivatives

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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 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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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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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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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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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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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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