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ICCSIP: An inexact chance-constrained semi-infinite programming approach for energy systems planning under uncertainty

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ENERGY SOURCES PART A-RECOVERY UTILIZATION AND ENVIRONMENTAL EFFECTS 2008年第14-15期30卷 1345-1366页

作者： Guo, P. Huang, G. H. He, L. Cai, Y. P. Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada Univ Waterloo Dept Civil & Environm Engn Waterloo ON N2L 3G1 Canada Beijing Normal Univ Chinese Res Acad Environm Sci Beijing 100875 Peoples R China

This article developed an inexact chance-constrained semi-infinite programming (ICCSIP) method for the energy management system under functional interval uncertainties. The approach not only considers the left-hand interval parameters, right-hand distribution information, and the probability of violating constraint, but also deals with functional interval uncertainty, which extends the range of the uncertainties. A regional energy management system is applied to illustrate the applicability of the ICCSIP approach. In consideration of energy sources allocation, fuel prices, and environmental regulations, a systematic planning of the regional energy structure is desired to bring a significant increase of economic benefit and improvement of environmental quality. This problem can be formulated as a programming model with an objective of minimizing the overall system costs subject to a number of environmental, economic and energy sources availability constraints. The programming results indicate that reasonable and useful decision alternatives can be generated under different probabilities of violating the system constraints. The obtained results are useful for decision makers to gain an insight into the tradeoffs among environmental, economic and system reliability criteria.

关键词： chance-constrained programming energy management system functional interval semi-infinite programming uncertainty

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Generalized semi-infinite programming: the Symmetric Reduction Ansatz

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OPTIMIZATION LETTERS 2008年第3期2卷 415-424页

作者： Guenzel, H. Jongen, H. Th. Stein, O. Univ Karlsruhe Sch Econ & Business Engn D-76128 Karlsruhe Germany Rhein Westfal TH Aachen Dept Math D-52056 Aachen Germany

We introduce the Symmetric Reduction Ansatz at a point from the closure of the feasible set in generalized semi-infinite programming. A corresponding Symmetric Reduction Lemma is shown for the local description of the latter set, and optimality conditions as well as topological properties are derived. We conjecture that the Symmetric Reduction Ansatz holds at all local minimizers of generic generalized semi-infinite programs.

关键词： semi-infinite programming Reduction Ansatz Reduction Lemma Optimality conditions

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A semi-infinite programming algorithm for solving optimal power flow with transient stability constraints

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第2期217卷 432-447页

作者： Tong, Xiaojiao Ling, Chen Qi, Liqun Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China Zhejiang Univ Finance & Econ Sch Math & Stat Hangzhou Zhejiang Peoples R China Changsha Univ Sci & Technol Inst Math Changsha Hunan Peoples R China

This paper proposes a new algorithm for solving a type of complicated optimal power flow (OPF) problems in power systems, i.e., OPF problems with transient stability constraints (OTS). The OTS is converted into a semi-infinite programming (SIP) via some suitable function analysis. Then based on the KKT system of the reformulated SIP, a smoothing quasi-Newton algorithm is presented in which the numerical integration is used. The convergence of the algorithm is established. An OTS problem in power system is tested, which shows that the proposed algorithm is promising. (C) 2007 Elsevier B.V. All rights reserved.

关键词： optimal power flow transient stability constraint semi-infinite programming quasi-Newton algorithm

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A norm-relaxed method of feasible directions for finely discretized problems from semi-infinite programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第1期186卷 41-62页

作者： Jian, Jin-Bao Xu, Qing-Juan Han, Dao-Lan Guangxi Univ Coll Math & Informat Sci Nanning 530004 Peoples R China Guangxi Teachers Educ Univ Dept Math & Comp Sci Nanning 530001 Peoples R China Guangxi Univ Coll Math & Comp Sci Nanning 530006 Peoples R China

In this paper, a class of finely discretized semi-infinite programming (SIP) problems is discussed. Combining the idea of the norm-relaxed Method of Feasible Directions (MFD) and the technique of updating discretization index set, we present a new algorithm for solving the Discretized semi-infinite (DSI) problems from SIP. At each iteration, the iteration point is feasible for the discretized problem and an improved search direction is computed by solving only one direction finding subproblem, i.e., a quadratic program, and some appropriate constraints are chosen to reduce the computational cost. A high-order correction direction can be obtained by solving another quadratic programming subproblem with only equality constraints. Under weak conditions such as Mangasarian-Fromovitz Constraint Qualification (MFCQ), the proposed algorithm possesses weak global convergence. Moreover, the superlinear convergence is obtained under Linearly Independent Constraint Qualification (LICQ) and other assumptions. In the end, some elementary numerical experiments are reported. (c) 2007 Elsevier B.V. All rights reserved.

关键词： semi-infinite programming norm-relaxed method of feasible direction global convergence superlinear convergence

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ISMISIP: an inexact stochastic mixed integer linear semi-infinite programming approach for solid waste management and planning under uncertainty

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2008年第6期22卷 759-775页

作者： Guo, P. Huang, G. H. He, L. N China Elect Power Univ Chinese Res Acad Environm Sci Beijing 100012 Peoples R China Univ Regina Environm Syst Engn Program Regina SK S4S 0A2 Canada Univ Regina Ctr Energy & Environm Studies Regina SK S4S 0A2 Canada

An inexact stochastic mixed integer linear semi-infinite programming (ISMISIP) model is developed for municipal solid waste (MSW) management under uncertainty. By incorporating stochastic programming (SP), integer programming and interval semi-infinite programming (ISIP) within a general waste management problem, the model can simultaneously handle programming problems with coefficients expressed as probability distribution functions, intervals and functional intervals. Compared with those inexact programming models without introducing functional interval coefficients, the ISMISIP model has the following advantages that: (1) since parameters are represented as functional intervals, the parameter's dynamic feature (i.e., the constraint should be satisfied under all possible levels within its range) can be reflected, and (2) it is applicable to practical problems as the solution method does not generate more complicated intermediate models (He and Huang, Technical Report, 2004;He et al. J Air Waste Manage Assoc, 2007). Moreover, the ISMISIP model is proposed upon the previous inexact mixed integer linear semi-infinite programming (IMISIP) model by assuming capacities of the landfill, WTE and composting facilities to be stochastic. Thus it has the improved capabilities in (1) identifying schemes regarding to the waste allocation and facility expansions with a minimized system cost and (2) addressing tradeoffs among environmental, economic and system reliability level.

关键词： chance-constrained programming decision making functional interval semi-infinite programming uncertainty

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Generalized semi-infinite programming:: On generic local minimizers

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JOURNAL OF GLOBAL OPTIMIZATION 2008年第3期42卷 413-421页

作者： Guenzel, Harald Jongen, Hubertus Th. Stein, Oliver Rhein Westfal TH Aachen Dept Math D-52056 Aachen Germany Univ Karlsruhe Dept Econ D-76128 Karlsruhe Germany

In this paper a basic structural problem in Generalized semi-infinite programming is solved. In fact, under natural and generic assumptions we show that at any (local) minimizer the "Symmetric Reduction Ansatz&qu... 详细信息

关键词： semi-infinite programming optimality condition reduction ansatz

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Application of general semi-infinite programming to lapidary cutting problems

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2008年第3期191卷 838-854页

作者： Winterfeld, Anton Fraunhofer Inst Ind Math ITWM Dept Optimizat D-67663 Kaiserslautern Germany

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interior-point method developed by Stein [O. Stein, Bi-level Strategies in semi-infinite programming, Kluwer Academic Publishers, Boston, 2003]. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on real-world data are also presented. (C) 2007 Elsevier B.V. All rights reserved.

关键词： large scale optimization semi-infinite programming nonlinear programming design centering

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Optimum design of discrete-time differentiators via semi-infinite programming approach

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT 2008年第10期57卷 2226-2230页

作者： Ho, Charlotte Yuk-Fan Ling, Bingo Wing-Kuen Liu, Yan-Qun Tam, Peter Kwong-Shun Teo, Kok-Lay Queen Mary Univ London Sch Math Sci London E1 4NS England Kings Coll London Dept Elect Engn Div Engn London WC2R 2LS England RMIT Univ Dept Math & Stat Melbourne Vic 3001 Australia Hong Kong Polytech Univ Elect & Informat Engn Dept Kowloon Hong Kong Peoples R China Curtin Univ Technol Dept Math & Stat Perth WA 6845 Australia

In this paper, a general optimum full-band, high-order discrete-time differentiator design problem is formulated as a peak-constrained least squares optimization problem. That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted error function. This problem formulation provides great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator. The optimization problem is actually a semi-infinite programming,problem. Our recently developed dual parameterization algorithm is applied to solve the problem. The main advantages of employing the dual parameterization algorithm to solve the problem are as follows: 1) the guarantee of the convergence of the algorithm and 2) the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms that are implementing the semidefinite programming approach.

关键词： discrete-time differentiators dual parameterization algorithm eigen approach peak-constrained least squares approach Remez approach semidefinite programming approach semi-infinite programming

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Portfolios with fuzzy returns: Selection strategies based on semi-infinite programming

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第2期217卷 381-393页

作者： Vercher, Enriqueta Univ Valencia Fac Matemat Dept Estadist & IO E-46100 Burjassot Spain

This paper provides new models for portfolio selection in which the returns on securities are considered fuzzy numbers rather than random variables. The investor's problem is to find the portfolio that minimizes the risk of achieving a return that is not less than the return of a riskless asset. The corresponding optimal portfolio is derived using semi-infinite programming in a soft framework. The return on each asset and their membership functions are described using historical data. The investment risk is approximated by mean intervals which evaluate the downside risk for a given fuzzy portfolio. This approach is illustrated with a numerical example. (C) 2007 Elsevier B.V. All rights reserved.

关键词： fuzzy mathematical programming fuzzy returns downside risk function portfolio selection problem semi-infinite programming

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Some results on Lipschitz properties of the optimal values in semi-infinite programming

Some results on Lipschitz properties of the optimal values i...

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2nd International Conference on Optimization Methods and Software/6th EUROPT Workshop on Advances in Continuous Optimization

作者： Toledo, F. J. Miguel Hernandez Univ Elche Ctr Operat Res Alicante Spain

This paper studies certain Lipschitz properties of the optimal value function of a linear semi-infinite programming problem and its dual problem in the sense of Haar. In this setting, it is already known that the optimal value function of the so-called primal problem was Lipschitz continuous around a given stable solvable problem, when perturbations of all the coefficients are allowed. Recently, a Lipschitz constant, depending only on the nominal problem data, has been computed and, the no duality gap under certain stability conditions ensures moreover that the obtained constant still holds for the dual optimal value function. Our approach here is focused on obtaining Lipschitz constants for both primal and dual optimal value functions under weaker hypothesis of stability, which do not preclude, in all the cases, the existence of duality gap. Now, the allowed perturbations are restricted to the coefficients of the objective function of the corresponding problems.

关键词： semi-infinite programming Lipschitz properties optimal value

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