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The Direct Solution of Nonconvex Nonlinear FIR Filter Design Problems by a SIP Method

OPTIMIZATION AND ENGINEERING 2000年第2期1卷 123-154页

作者： Goerner, Stephan Potchinkov, Alexander Reemtsen, Rembert Univ Kaiserslautern Fachbereich Elektrotech D-67763 Kaiserslautern Germany Brandenburg Tech Univ Cottbus Inst Mathemat D-03044 Cottbus Germany

FIR filter design problems in the frequency domain are nonlinear (semi-infinite) optimization problems. In practice, however, these almost always have not been approached directly, but been solved in a simplified form and/or only under restricting assumptions. In this paper, quite general mathematical formulations of the four main design approximation problems in the frequency domain are presented, which enable the derivation of theoretical results (collected here from R. Reemtsen, 2000b, 2000c) and the application of general-purpose optimization procedures to their direct solution. For the actual solution, a nonlinear semi-infinite programming method from the thesis (S. Gorner, Ph.D. Thesis, Technische Universitat Berlin, Berlin, 1997) of the first author is discussed and applied to several specific design problems. In some cases, the computed solution of the nonlinear problem is compared with that of a convex approximation of the problem.

关键词： filter design FIR filters semi-infinite programming SQP methods

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Uncertainty modelling and robust output feedback control of nonlinear discrete systems: a mathematical programming approach

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2000年第13期10卷 1129-1152页

作者： Slupphaug, O Imslands, L Foss, BA Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway

We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter-dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite) series of ordinary linear programs. Additionally, the system representation includes control and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter-dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this non-convex feasibility problem is proposed. Complexity of the design method and some special cases such as state feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state-feedback model predictive control with robust stability. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： robust control constrained control affine parameter-dependent models bilinear matrix inequalities semi-infinite programming nonlinear model predictive control

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

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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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A semi-infinite programming model for earliness/tardiness production planning with simulated annealing

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MATHEMATICAL AND COMPUTER MODELLING 1997年第7期26卷 35-42页

作者： Li, Y Wang, D NORTHEASTERN UNIV DEPT AUTOMAT CONTROLSHENYANG 110006PEOPLES R CHINA

To describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi-infinite programming model was proposed in [1]. Due to a nonconvex objective function and infinitely many constraints, the model is difficult to solve by traditional methods. In this paper, simulated annealing method combined with a heuristic and the steepest descent method is developed. Numerical results shows that the present approach is very efficient. In theory, the developed method is an attempt to solve a continuous domain problem by simulated annealing.

关键词： earliness/tardiness schedule semi-infinite programming heuristic simulated annealing

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Logarithmic barrier decomposition methods for semi-infinite programming

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International Transactions in Operational Research 1997年第4期4卷 285-303页

作者： Kaliski, J. Haglin, D. Roos, C. Terlaky, T. Mankato State University United States Drlft University of Technology Netherlands

A computational study of some logarithmic barrier decomposition algorithms for semi-infinite programming is presented in this paper. The conceptual algorithm is a straightforward adaptation of the logarithmic barrier cutting plane algorithm which was presented recently by den Hartog et al. (Annals of Operations Research, 58, 69-98, 1995), to solve semi-infinite programming problems. Usually decomposition (cutting plane methods) use cutting planes to improve the localization of the given problem. In this paper we propose an extension which uses linear cuts to solve large scale, difficult real world problems. This algorithm uses both static and (doubly) dynamic enumeration of the parameter space and allows for multiple cuts to be simultaneously added for larger/difficult problems. The algorithm is implemented both on sequential and parallel computers. Implementation issues and parallelization strategies are discussed and encouraging computational results are presented. © 1997 Blackwell Publishing Ltd.

关键词： Column generation Convex programming Cutting plane methods Interior point method Linear programming Logarithmic barrier function Quadratic programming semi-infinite programming

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A dual approach to continuous-time envelope-constrained filter design via orthonormal filters

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS 1999年第9期46卷 1042-1054页

作者： Tseng, CH Teo, KL Zang, ZQ Cantoni, A Curtin Univ Technol Telecom Australia Res Labs Perth WA 6845 Australia Hong Kong Polytech Univ Dept Appl Mech Kowloon Peoples R China

The envelope constrained (EC) filtering problem was initially posed in the continuous-time domain as a constrained L-2 space optimization problem. However, only the discretized version has been solved, using various approaches. In this paper me consider the continuous-time EC filtering problem formulated using an orthonormal basis defined on a Hilbert vector space. Caratheodory's theorem and the dual parametrization method are used to obtain a dual finite-dimensional optimization problem, Two iterative algorithms based on the gradient flow technique are then developed for solving this dual problem. The design of an EC optimal equalization filter for a communication channel is solved to illustrate the effectiveness of the proposed algorithm.

关键词： Caratheodory's dimensional method continuous-time filters duality envelope constraints gradient flow Hilbert spaces Laguerre processes semi-infinite programming space transformation

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Combined entropic regularization and path-following method for solving finite convex min-max problems subject to infinitely many linear constraints

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第1期101卷 167-190页

作者： Sheu, RL Wu, SY Natl Cheng Kung Univ Tainan 70101 Taiwan

In this paper, we study the minimization of the max function of q smooth convex functions on a domain specified by infinitely many linear constraints. The difficulty of such problems arises from the kinks of the max function and it is often suggested that, by imposing certain regularization functions, nondifferentiability will be overcome. We find that the entropic regularization introduced by Li and Fang is closely related to recently developed path-following interior-point methods. Based on their results, we create an interior trajectory in the feasible domain and propose a path-following algorithm with a convergence proof. Our intention here is to show a nice combination of minmax problems, semi-infinite programming, and interior-point methods, Hopefully, this will lead to new applications.

关键词： min-max problems entropic regularization nonsmooth optimization interior-point methods path-following methods semi-infinite programming

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Analytical linear inequality systems and optimization

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第1期103卷 95-119页

作者： Goberna, MA Jornet, V Puente, R Todorov, MI Univ Alicante Fac Sci Dept Stat & Operat Res E-03080 Alicante Spain Natl Univ San Luis Fac Phys Math & Nat Sci Dept Math San Luis Argentina Bulgarian Acad Sci Inst Math Plovdiv Bulgaria

In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.

关键词： linear inequality systems convex sets semi-infinite programming purification algorithms

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Second order optimality conditions based on parabolic second order tangent sets

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SIAM JOURNAL ON OPTIMIZATION 1999年第2期9卷 466-492页

作者： Bonnans, JF Cominetti, R Shapiro, A Inst Natl Rech Informat & Automat F-78153 Rocquencourt France Univ Chile Santiago Chile Georgia Inst Technol Sch Ind & Syst Engn Atlanta GA 30332 USA

In this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints. Our analysis is based on various concepts of second order tangent sets and parametric duality. We introduce a condition, called second order regularity, under which there is no gap between the corresponding second order necessary and second order sufficient conditions. We show that the second order regularity condition always holds in the case of semidefinite programming.

关键词： second order optimality conditions semidefinite programming semi-infinite programming tangent sets Lagrange multipliers cone constraints duality

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A semi-infinite programming model for earliness tardiness production planning with a genetic algorithm

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 1996年第8期31卷 95-106页

作者： Wang, DW Fang, SC N CAROLINA STATE UNIV RALEIGH NC 27695 USA

To closely describe the earliness/tardiness production planning problems in the JIT environment, a nonlinear semi-infinite programming model is proposed. Due to the issues of nonconvexivity and having infinitely many constraints, instead of applying traditional optimization approaches, a specially designed genetic algorithm with mutation along the negative gradient direction is developed. The proposed algorithm is a combination of the steepest descent method with the stochastic sampling algorithm. Some numerical results are included to show its potential for industrial applications.

关键词： production planning earliness/tardiness schedule genetic algorithm semi-infinite programming

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