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An interval full-infinite programming method to supporting environmental decision-making

ENGINEERING OPTIMIZATION 2008年第8期40卷 709-728页

作者： He, L. Huang, G. H. Tan, Q. Liu, Z. F. Univ Regina Fac Engn Regina SK S4S 0A2 Canada N China Elect Power Univ Chinese Res Acad Environm Sci Beijing 100012 Peoples R China

An interval full-infinite programming (IFIP) method is developed by introducing a concept of functional intervals into an optimization framework. Since the solutions of the problem should be 'globally' optimal under all possible levels of the associated impact factors, the number of objectives and constraints is infinite. To solve the IFIP problem, it is converted to two interactive semi-infinite programming (SIP) submodels that can be solved by conventional SIP solution algorithms. The IFIP method is applied to a solid waste management system to illustrate its performance in supporting decision-making. Compared to conventional interval linear programming (ILP) methods, the IFIP is capable of addressing uncertainties arising from not only the imprecise information but also complex relations to external impact factors. Compared to SIP that can only handle problems containing infinite constraints, the IFIP approaches are useful for addressing inexact problems with infinite objectives and constraints.

关键词： interval full-infinite programming semi-infinite programming uncertainty functional interval environmental decision

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Cascading: an adjusted exchange method for robust conic programming

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2008年第2期16卷 179-189页

作者： Werner, Ralf Hypo Real Estate Holding AG Grp Risk Control D-80538 Munich Germany

It is well known that the robust counterpart introduced by Ben-Tal and Nemirovski (Math Oper Res 23:769-805, 1998) increases the numerical complexity of the solution compared to the original problem. Kocvara, Nemirovski and Zowe therefore introduced in Kocvara et al. (Comput Struct 76:431-442, 2000) an approximation algorithm for the special case of robust material optimization, called cascading. As the title already indicates, we will show that their method can be seen as an adjustment of standard exchange methods to semi-infinite conic programming. We will see that the adjustment can be motivated by a suitable reformulation of the robust conic problem.

关键词： robust programming conic programming semi-infinite programming exchange method

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Cascading: an adjusted exchange method for robust conic programming

Cascading: an adjusted exchange method for robust conic prog...

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5th Europe Workshop on Advances in Continuous Optimization

作者： Werner, Ralf Hypo Real Estate Holding AG Grp Risk Control D-80538 Munich Germany

关键词： robust programming conic programming semi-infinite programming exchange method

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Shakedown analysis of spatial frames with parameterized load domain

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ENGINEERING STRUCTURES 2008年第11期30卷 3119-3128页

作者： Bisbos, C. D. Ampatzis, A. T. Aristotle Univ Thessaloniki Dept Civil Engn Inst Steel Struct GR-54124 Thessaloniki Greece

This work addresses shakedown analysis of geometrically linear spatial frames with linearized yield criteria and parameterized general variable load domain. If the boundary of the load domain is curved, the respective optimization problem has an infinite number of constraints. Using parameterization a, computational bi-level decomposition methodology is developed, which is capable of treating problems of this kind. Two alternative bi-level procedures are presented: the centered minmax technique and the parameterized Maier's technique. The lower level, shared by both procedures, comprises a series of local constrained optimization problems for the check points across the frame. These low-order problems, solved either algorithmically or analytically, provide data for the upper level, where a linear programming problem of limit analysis type is solved in each procedure for the whole frame. Two examples with ellipsoidal load domain are presented. Several aspects are discussed. (C) 2008 Elsevier Ltd. All rights reserved.

关键词： Plasticity Shakedown Frames semi-infinite programming Bi-level decomposition

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ON EXTENSION OF FENCHEL DUALITY AND ITS APPLICATION

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SIAM JOURNAL ON OPTIMIZATION 2008年第3期19卷 1489-1509页

作者： Li Guoyin Fu, Ng Kung Chinese Univ Hong Kong Dept Math Shatin Hong Kong Peoples R China

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given ... 详细信息

关键词： Fenchel duality epigraph Karush-Kuhn-Tucker (KKT) conditions semi-infinite programming

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An interior point algorithm for continuous minimax: implementation and computation

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OPTIMIZATION METHODS & SOFTWARE 2008年第6期23卷 911-928页

作者： Rustem, B. Zakovic, S. Parpas, P. Univ London Imperial Coll Sci Technol & Med Dept Comp London England

In this paper, we propose an algorithm for the constrained continuous minimax problem. The algorithm, motivation, and numerical experience are reported in this paper. Theoretical properties and the convergence of the proposed method are discussed in a separate paper [B. Rustem, S. Zakovic, and P. Parpas, Convergence of an interior point algorithm for continuous minimax, J. Optim. Theory Appl. (2007), in press]. The algorithm uses quasi-Newton search direction, based on sub-gradient information, conditional on maximizers. The initial problem is transformed to an equivalent equality constrained problem, where the logarithmic barrier function is used to ensure feasibility. In the case of multiple maximizers, the algorithm adopts semi-infinite programming iterations towards epi-convergence. Satisfaction of the equality constraints is ensured by an adaptive quadratic penalty function. The algorithm is augmented by a discrete minimax procedure to compute the semi-infinite programming steps and ensure overall progress when required by the adaptive penalty procedure. Progress towards the solution is maintained using merit functions. Computational results are included to illustrate the efficient performance of the algorithm.

关键词： continuous minimax interior point algorithms semi-infinite programming epi-convergence

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THE EXACT FEASIBILITY OF RANDOMIZED SOLUTIONS OF UNCERTAIN CONVEX PROGRAMS

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SIAM JOURNAL ON OPTIMIZATION 2008年第3期19卷 1211-1230页

作者： Campi, M. C. Garatti, S. Univ Brescia Dipartimento Elettron Automaz I-25123 Brescia Italy Politecn Milan Dipartimento Elettron & Informaz I-20133 Milan Italy

Many optimization problems are naturally delivered in an uncertain framework, and one would like to exercise prudence against the uncertainty elements present in the problem. In previous contributions, it has been shown that solutions to uncertain convex programs that bear a high probability to satisfy uncertain constraints can be obtained at low computational cost through constraint randomization. In this paper, we establish new feasibility results for randomized algorithms. Specifically, the exact feasibility for the class of the so-called fully-supported problems is obtained. It turns out that all fully-supported problems share the same feasibility properties, revealing a deep kinship among problems of this class. It is further proven that the feasibility of the randomized solutions for all other convex programs can be bounded based on the feasibility for the prototype class of fully-supported problems. The feasibility result of this paper outperforms previous bounds and is not improvable because it is exact for fully-supported problems.

关键词： uncertain optimization randomized methods convex optimization semi-infinite programming robust optimization chance-constrained

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Numerical method for a class of optimal control problems subject to nonsmooth functional constraints

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第2期217卷 311-325页

作者： Wu, C. Z. Teo, K. L. Zhao, Yi Curtin Univ Technol Dept Math & Stat Perth WA Australia Chongqing Normal Univ Sch Math & Comp Sci Chongqing 400047 Peoples R China

In this paper, we consider a class of optimal control problems which is governed by nonsmooth functional inequality constraints involving convolution. First, we transform it into an equivalent optimal control problem with smooth functional inequality constraints at the expense of doubling the dimension of the control variables. Then, using the Chebyshev polynomial approximation of the control variables, we obtain an semi-infinite quadratic programming problem. At last, we use the dual parametrization technique to solve the problem. (C) 2007 Elsevier B.V. All rights reserved.

关键词： optimal control functional inequality constraints semi-infinite programming Chebyshev series dual parametrization

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Convergence of an interior point algorithm for continuous minimax

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2008年第1期136卷 87-103页

作者： Rustem, B. Zakovic, S. Parpas, P. Univ London Imperial Coll Sci Technol & Med Dept Comp London England

We propose an algorithm for the constrained continuous minimax problem. The algorithm uses a quasi-Newton search direction, based on subgradient information, conditional on maximizers. The initial problem is transformed to an equivalent equality constrained problem, where the logarithmic barrier function is used to ensure feasibility. In the case of multiple maximizers, the algorithm adopts semi-infinite programming iterations toward epiconvergence. Satisfaction of the equality constraints is ensured by an adaptive quadratic penalty function. The algorithm is augmented by a discrete minimax procedure to compute the semi-infinite programming steps and ensure overall progress when required by the adaptive penalty procedure. Progress toward the solution is maintained using merit functions.

关键词： worst case analysis continuous minimax algorithms interior point methods semi-infinite programming

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Stability of the intersection of solution sets of semi-infinite systems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第2期217卷 420-431页

作者： Goberna, Miguel A. Larriqueta, Mercedes Vera de Serio, Virginia N. Univ Alicante Dept Estadist & Invest Operat Alicante Spain Univ Nacl Cuyo Fac Ingn RA-5500 Mendoza Argentina Univ Nacl Cuyo Fac Ciencias Econ RA-5500 Mendoza Argentina

Many mathematical programming models arising in practice present a block structure in their constraint systems. Consequently, the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not. The existence theorems allow to decide when the intersection of non-empty sets in the Euclidean space, which are the solution sets of systems of (possibly infinite) inequalities, is empty or not. In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the sets is preserved by sufficiently small perturbations or not. This paper focuses on the stability of the non-empty (empty) intersection of the solutions of some given systems, which can be seen as the images of set-valued mappings. We give sufficient conditions for the stability, and necessary ones as well;in particular we consider (semi-infinite) convex systems and also linear systems. In this last case we discuss the distance to ill-posedness. (C) 2007 Elsevier B.V. All rights reserved.

关键词： set-valued mappings stability theory semi-infinite programming

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