An original method is presented to solve the parametric linear complementarity problem. To solve such a problem requires to identify the values taken by the solution of a linear complementarity problem where some of i...
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An original method is presented to solve the parametric linear complementarity problem. To solve such a problem requires to identify the values taken by the solution of a linear complementarity problem where some of its right-hand side terms vary in a prescribed domain. This class of problems allows, among others, to deal with linear market equilibrium problems with varying prices: it allows to identify how does the equilibrium point varies when the prices vary over a set of given values. This method is illustrated through an application related to the institution of ecological taxes on the Western European natural gas market. (C) 2001 Elsevier Science B.V. All rights reserved.
Recently, O(n(2)) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x' Dx - a'x + lambda/gamma'x - c\ and (1/2)x' Dx - a'x + (lambda/2)(gamma'x - c)(...
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Recently, O(n(2)) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x' Dx - a'x + lambda/gamma'x - c\ and (1/2)x' Dx - a'x + (lambda/2)(gamma'x - c)(2), respectively, subject to l less than or equal to x less than or equal to b, for all nonnegative values of the parameter lambda. Here, D is a positive diagonal n x n matrix, gamma and a are arbitrary n-vectors, c is an arbitrary scalar;l and b are arbitrary n-vectors such that l less than or equal to b. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs with no additional computational cost.
In this paper the application of parametric programming to CNC machining is discussed. As one of the less frequently utilized features of CNC machines, parametric programming has the potential to increase the efficien...
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In this paper the application of parametric programming to CNC machining is discussed. As one of the less frequently utilized features of CNC machines, parametric programming has the potential to increase the efficiency of CNC operations. This feature is particularly beneficial to companies with group technology manufacturing where parts with similar design or operational requirements are processed within a machine cell. Using two case studies, the capabilities of parametric programming for CNC machines are illustrated. (C) 1998 Elsevier Science Ltd. All rights reserved.
The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the constraint matrix is a family of 0-1-ILP problems in which the problems are related by having identical objective and right-hand-sid...
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The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the constraint matrix is a family of 0-1-ILP problems in which the problems are related by having identical objective and right-hand-side vectors. In this paper we present an algorithm to perform a complete multiparametric analysis. (C) 2000 Elsevier Science B.V. All rights reserved.
The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the objective function is a family of 0-1-ILP problems in which the problems are related by having identical constraint matrix and right...
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The multiparametric 0-1-Integer Linear programming (0-1-ILP) problem relative to the objective function is a family of 0-1-ILP problems in which the problems are related by having identical constraint matrix and right-hand side vector. In this paper we present an algorithm to perform a complete multiparametric analysis. (C) 2000 Elsevier Science B.V. All rights reserved.
This paper describes two new, mathematical programming-based approaches for evaluating general, one- and two-sided, p-variate normal probabilities where the variance-covariance matrix (of arbitrary structure) is singu...
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This paper describes two new, mathematical programming-based approaches for evaluating general, one- and two-sided, p-variate normal probabilities where the variance-covariance matrix (of arbitrary structure) is singular with rank r(r < p), and r and p can be of unlimited dimensions. In both cases, principal components are used to transform the original, ill-defined, p-dimensional integral into a well-defined, r-dimensional integral over a convex polyhedron. The first algorithm that is presented uses linear programming coupled with a Gauss-Legendre quadrature scheme to compute this integral, while the second algorithm uses multi-parametric programming techniques in order to significantly reduce the number of optimization problems that need to be solved. The application of the algorithms is demonstrated and aspects of computational performance are discussed through a number of examples, ranging from a practical problem that arises in chemical engineering to larger, numerical examples.
The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal w...
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The existing data envelopment analysis (DEA) models for measuring the relative efficiencies of a set of decision making units (DMUs) using various inputs to produce various outputs are limited to crisp data. To deal with imprecise data, the notion of fuzziness has been introduced. This paper develops a procedure to measure the efficiencies of DMUs with fuzzy observations. The basic idea is to transform a fuzzy DEA model to a family of conventional crisp DEA models by applying the a-cut approach. A pair of parametric programs is formulated to describe that family of crisp DEA models, via which the membership functions of the efficiency measures are derived. Since the efficiency measures are expressed by membership functions rather than by crisp values, more information is provided for management. By extending to fuzzy environment, the DEA approach is made more powerful for applications. (C) 2000 Elsevier Science B.V. All rights reserved.
A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to tak...
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A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of eta -dimensional closed balls B-r(eta) (p), which are defined by means of a p-norm and a radius vector parameter r. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c-parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations(required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.
This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have bee...
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This paper establishes theorems about the simultaneous variation of right-hand sides and cost coefficients in a linear program from a strictly complementary solution. Some results are extensions of those that have been proven for varying the right-hand side of the primal or the dual, but not both;other results are new. In addition, changes in the optimal partition and what that means in economic terms are related to the basis-driven approach, notably to the theory of compatibility. In addition to new theorems about this relation, the transition graph is extended to provide another visualization of the underlying economics.
This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results con...
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This paper deals with multiobjective nonlinear programming problems with random variables in the objective functions. These random variables are characterized by possibility density functions. The existing results concerning the qualitative analysis of basic notions in parametric nonlinear programming problems are reformulated to study the stability sets of the first, second, third and fourth kind for multiobjective nonlinear programming problems under the concept of a-possibility efficient. (C) 1999 Elsevier Science B.V. All rights reserved.
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