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Design of optimal linear phase FIR filters by a semi-infinite programming technique

SIGNAL PROCESSING 1997年第2期58卷 165-180页

作者： Potchinkov, AW Technische Universität Cottbus Lehrstuhl für Ingenieurmathematik I Fakultät 1 Postfach 101344 D-03013 Cottbus Germany

The topic of this paper is the design of optimal linear phase FIR filters by means of semi-infinite programming technique. The filters are specified primarily in the frequency domain and can be additionally constrained with respect to the time domain, The new method allows constrained and unconstrained minimax- and also least-squares designs. In this way, it completely substitutes several other current methods which allows the filter designer to develop a large variety of filter designs by using a single computer program. Highly accurate solutions with up to around 2000 filter coefficients demonstrate several of the abilities of the new method. (C) 1997 Elsevier Science B.V.

关键词： linear phase FIR filter design constrained approximation minimax and least squares filters optimization semi-infinite programming

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On saddle points in nonconvex semi-infinite programming

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JOURNAL OF GLOBAL OPTIMIZATION 2012年第3期54卷 433-447页

作者： Guerra-Vazquez, Francisco Rueckmann, Jan-J Werner, Ralf Univ Amer Escuela Ciencias Puebla 72820 Mexico Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England Munich Univ Appl Sci D-80335 Munich Germany

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems.

关键词： semi-infinite programming Lagrangian function (Partial)P-power formulation Local convexification Duality

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Second-Order Optimality Conditions and Duality for Multiobjective semi-infinite programming Problems on Hadamard Manifolds

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ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2024年第2期41卷

作者： Upadhyay, Balendu Bhooshan Ghosh, Arnav Stancu-Minasian, I. M. Indian Inst Technol Patna Dept Math Bihta Bihar India Romanian Acad Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl M Bucharest Romania

This paper is devoted to the study of multiobjective semi-infinite programming problems on Hadamard manifolds. We consider a class of multiobjective semi-infinite programming problems (abbreviated as MSIP) on Hadamard manifolds. We use the concepts of second-order Karush-Kuhn-Tucker stationary point and second-order Karush-Kuhn-Tucker geodesic pseudoconvexity of the considered problem to derive necessary and sufficient second-order conditions of efficiency, weak efficiency and proper efficiency for MSIP along with certain generalized geodesic convexity assumptions. Moreover, we formulate the second-order Mond-Weir-type dual problem related to MSIP and deduce weak and strong duality theorems relating MSIP and the dual problem. The significance of our results is demonstrated with the help of non-trivial examples. To the best of our knowledge, this is the first time that second-order optimality conditions for MSIP have been studied in Hadamard manifold setting.

关键词： semi-infinite programming multiobjective optimization second-order optimality duality Hadamard manifolds

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New extremal principles with applications to stochastic and semi-infinite programming

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MATHEMATICAL programming 2021年第1-2期189卷 527-553页

作者： Mordukhovich, Boris S. Perez-Aros, Pedro Wayne State Univ Dept Math Detroit MI 48202 USA Univ OHiggins Inst Ciencias Ingn Rancagua Chile

This paper develops new extremal principles of variational analysis that are motivated by applications to constrained problems of stochastic programming and semi-infinite programming without smoothness and/or convexity assumptions. These extremal principles concern measurable set-valued mappings/multifunctions with values in finite-dimensional spaces and are established in both approximate and exact forms. The obtained principles are instrumental to derive via variational approaches integral representations and upper estimates of regular and limiting normals cones to essential intersections of sets defined by measurable multifunctions, which are in turn crucial for novel applications to stochastic and semi-infinite programming.

关键词： Variational analysis Generalized differentiation Normal cone calculus Stochastic programming semi-infinite programming

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Constrained incremental bundle method with partial inexact oracle for nonsmooth convex semi-infinite programming problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2016年第2期64卷 433-465页

作者： Pang, Li-Ping Lv, Jian Wang, Jin-He Dalian Univ Technol Sch Math Sci Dalian 116024 Peoples R China Qingdao Technol Univ Sch Comp Engn Qingdao 266033 Peoples R China

semi-infinite problem (SIPs) are widely used in many control systems for solving complex control problem, such as polymerase chain reaction control system or other real time control system. In this paper, we present a bundle method for solving the nonsmooth convex SIPs, with the aim of working on the basis of "improvement function", "inexact oracle" and "incomplete knowledge" of the constraints. The proposed algorithm, whenever a new stabilized center is refreshed, requires an evaluation within some accuracy for the value of constraints. Beyond that, by using the incremental technique, it does not require all information about the constraints, but only one component function value and one subgradient needed to be estimated to update the bundle information and generate the search direction. Thus the computational cost is significantly reduced. Global convergence of this method is established based on some mild assumptions. Numerical experiments show that the algorithm is efficient for solving nonsmooth convex SIPs.

关键词： Constrained optimization Nonsmooth optimization semi-infinite programming Bundle method

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A semi-infinite programming approach to identifying matrix-exponential distributions

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2012年第9期43卷 1623-1631页

作者： Fackrell, Mark Univ Melbourne Dept Math & Stat Melbourne Vic 3010 Australia

The Laplace-Stieltjes transform of a matrix-exponential (ME) distribution is a rational function where at least one of its poles of maximal real part is real and negative. The coefficients of the numerator polynomial, however, are more difficult to characterise. It is known that they are contained in a bounded convex set that is the intersection of an uncountably infinite number of linear half-spaces. In order to determine whether a given vector of numerator coefficients is contained in this set (i.e. the vector corresponds to an ME distribution) we present a semi-infinite programming algorithm that minimises a convex distance function over the set. In addition, in the event that the given vector does not correspond to an ME distribution, the algorithm returns a closest vector which does correspond to one.

关键词： matrix-exponential distribution rational Laplace-Stieltjes transform semi-infinite programming

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A new exact penalty method for semi-infinite programming problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2014年 261卷 271-286页

作者： Lin, Qun Loxton, Ryan Teo, Kok Lay Wu, Yong Hong Yu, Changjun Curtin Univ Dept Math & Stat Perth WA 6845 Australia

In this paper, we consider a class of nonlinear semi-infinite optimization problems. These problems involve continuous inequality constraints that need to be satisfied at every point in an infinite index set, as well as conventional equality and inequality constraints. By introducing a novel penalty function to penalize constraint violations, we form an approximate optimization problem in which the penalty function is minimized subject to only bound constraints. We then show that this penalty function is exact that is, when the penalty parameter is sufficiently large, any local solution of the approximate problem can be used to generate a corresponding local solution of the original problem. On this basis, the original problem can be solved as a sequence of approximate nonlinear programming problems. We conclude the paper with some numerical results demonstrating the applicability of our approach to PID control and filter design. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Exact penalty function semi-infinite programming Constrained optimization Nonlinear programming

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CONDITIONS FOR THE UNIQUENESS OF THE OPTIMAL SOLUTION IN LINEAR semi-infinite programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1992年第2期72卷 225-246页

作者： GOBERNA, MA LOPEZ, MA 1. Faculty of Sciences University of Alicante Alicante Spain

In this paper, we establish different conditions for the uniqueness of the optimal solution of a semi-infinite programming problem. The approach here is based on the differentiability properties of the optimal value function and yields the corresponding extensions to the general linear semi-infinite case of many results provided by Mangasarian and others. In addition, detailed optimality conditions for the most general problem are supplied, and some features of the optimal set mapping are discussed. Finally, we obtain a dimensional characterization of the optimal set, provided that a usual closedness condition (Farkas-Minkowski condition) holds.

关键词： semi-infinite programming OPTIMALITY CONDITIONS OPTIMAL VALUE FUNCTION DIFFERENTIABLE CONVEX FUNCTIONS

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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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