It is demonstrated that the improvement achieved by using integerprogramming over simple coefficient rounding in the design of finite impulse response (FIR) filters with discrete coefficients is most significant when...
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It is demonstrated that the improvement achieved by using integerprogramming over simple coefficient rounding in the design of finite impulse response (FIR) filters with discrete coefficients is most significant when the discrete coefficient space is the powers-of-two space or when a specification is to be met with a given coefficient word length by increasing the filter length. Both minimax and least square error criteria are considered.
An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factorin...
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An algorithm is presented which reduces the problem of finding the irreducible factors of a bivariate polynomial with integer coefficients in polynomial time in the total degree and the coefficient lengths to factoring a univariate integer polynomial. Together with A. Lenstra's, H. Lenstra's and L. Lovasz' polynomial-time factorization algorithm for univariate integer polynomials and the author's multivariate to bivariate reduction the new algorithm implies the following theorem. Factoring a polynomial with a fixed number of variables into irreducibles, except for the constant factors, can be accomplished in time polynomial in the total degree and the size of its coefficients. The new algorithm can be generalized to reducing multivariate factorization directly to univariate factorization and to factoring multivariate polynomials with coefficients in algebraic number fields and finite fields in polynomial time.
This paper presents an algorithm (called the N&M algorithm) for solving pure-integer separable nonlinearprogramming problems with two constraints. The N&M algorithm uses surrogate constraints and solves a giv...
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This paper presents an algorithm (called the N&M algorithm) for solving pure-integer separable nonlinearprogramming problems with two constraints. The N&M algorithm uses surrogate constraints and solves a given problem by effectively generating values of surrogate multiplier (i.e., surrogate problems) and solving the surrogate problems. Examples show that the N&M algorithm is superior to dynamic programming using the Lagrange multiplier in terms of number of iterations and narrowness of gap.
HaytonK. (1981) A linearprogramming land selection model for structure planning: a case study of Tyne and Wear,Reg. Studies15,425–437. This paper outlines the development and use of a methodology for strategic plan ...
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HaytonK. (1981) A linearprogramming land selection model for structure planning: a case study of Tyne and Wear,Reg. Studies15,425–437. This paper outlines the development and use of a methodology for strategic plan generation and evaluation as used in the production of a structure plan for the county of Tyne and Wear. An integer linear programming model was formulated. This was used to select a number of sites according to the extent to which their development would result in the attainment of plan objectives as measured by a number of criteria. To produce solutions, constraints were progressively varied to determine the trade-offs being made between criteria. The final solution maximized the attainment of objectives according to their relative priorities, being explicit about the compromises being made. The use of such a multidimensional optimization model as the basis for a statutory plan represents a considerable development in planning ***. (1981) Modèle à programmation linéaire pour la sélection des terrains visant la planification dite “structure planning”: cas d'espèce de Tyne et Wear,Reg. Studies15,425–437. Cet article expose à grands traits le developpement et l'emploi d'une méthodologie visant l'élaboration et l'evaluation des schémas stratégiques dont on s'est servi dans la rédaction d'un schéma dit “structure plan” en Tyne et Wear. Un modèle à programmation linéaire en nombres entiers était formulé. Celui-là servait à sélectionner un nombre de terrains en fonction de leur importance dans la réalisation des objectifs du schéma, évaluée en termes de certains critères, au fur et à mesure que ces terrains-là puissent être développés. Pour engendrer des solutions, les contraintes étaient variées petit à petit dans le but de déterminer les échanges qui se sont effectués entre les critères particuliers. La solution définitive a maximisé la réalisation des objectifs en fonction de leurs priorités relatives, en précisant les concessions faites. L'em
A recent paper has investigated the use of integer linear programming for the design of Chebyshev-optimal finite wordlength FIR digital filters. We point out that for some time domain error norms, coefficient rounding...
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A recent paper has investigated the use of integer linear programming for the design of Chebyshev-optimal finite wordlength FIR digital filters. We point out that for some time domain error norms, coefficient rounding provides the best approximation to the infinite precision filter.
It is shown that the problem of determining the maximum amplitude limit cycle of a given period in a second order digital filter can be formulated as an integerlinear program. Unfortunately, for even moderate limit c...
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It is shown that the problem of determining the maximum amplitude limit cycle of a given period in a second order digital filter can be formulated as an integerlinear program. Unfortunately, for even moderate limit cycle periods, the ILP can require considerable CPU time. A more straightforward procedure is thus proposed, which considers all possible initial states, which can be a maximum amplitude state of a limit cycle. Results are presented which significantly reduce the number of states requiring consideration, thereby resulting in a computationally feasible algorithm.
Optimal allocation of redundancy in a series system with separately maintained repairable subsystems subject to multiple constraints is investigated for maximizing system reliability using simplex pattern search and s...
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Optimal allocation of redundancy in a series system with separately maintained repairable subsystems subject to multiple constraints is investigated for maximizing system reliability using simplex pattern search and separable programming. The constraints, besides the usual ones, include one based on s-expected busy periods of the maintenance facilities. A numerical example illustrates the method.
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