A class of set-valued mappings called linearly semi-open mappings is introduced which properly contains the class of linearly open set-valued mappings. A stability result for linearly semi-open mappings is established...
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A class of set-valued mappings called linearly semi-open mappings is introduced which properly contains the class of linearly open set-valued mappings. A stability result for linearly semi-open mappings is established. The main result is a Lyusternik type theorem. Sufficient conditions for linear semi-openness of processes are derived. To verify these conditions, the openness bounds of certain processes are computed. A representation of the openness bound of a locally Lipschitz function in a Clarke non-critical point is given. It is shown that continuous piecewise linear functions on R-n are linearly semi-open under certain algebraic conditions. (C) 2003 Elsevier B.V. All rights reserved.
A practical estimate on the credibility formula is presented, where a piecewise linear function is taken as the approximation of the prior distribution and applied to the credibility theory. The convergence of the app...
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A practical estimate on the credibility formula is presented, where a piecewise linear function is taken as the approximation of the prior distribution and applied to the credibility theory. The convergence of the approximation is analyzed. Simulation results for the lognormal-lognormal mixture show the effectiveness of the proposed estimate on the credibility. (C) 2003 Elsevier B.V. All rights reserved.
In this paper a nonlinear model predictive control (NMPC) based on a Wiener model with a piecewiselinear gain is presented. This approach retains all the interested properties of the classical linear model predictive...
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In this paper a nonlinear model predictive control (NMPC) based on a Wiener model with a piecewiselinear gain is presented. This approach retains all the interested properties of the classical linear model predictive control (MPC) and keeps computations easy to solve due to the canonical structure of the nonlinear gain. Some guidelines for the identification of the nominal model as well as the uncertainty bounds are discussed, and two examples that show the possibility of application of this control scheme to real life problems are presented. (C) 2002 Elsevier Ltd. All rights reserved.
piecewise linear function (PLF) is an important technique for solving polynomial and/or posynomial programming problems since the problems can be approximately represented by the PLF. The PLF can also be solved using ...
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piecewise linear function (PLF) is an important technique for solving polynomial and/or posynomial programming problems since the problems can be approximately represented by the PLF. The PLF can also be solved using the goal programming (GP) technique by adding appropriate linearization constraints. This paper proposes a modified GP technique to solve PLF with n terms. The proposed method requires only one additional constraint, which is more efficient than some well-known methods such as those proposed by Charnes and Cooper's, and Li. Furthermore, the proposed model (PM) can easily be applied to general polynomial and/or posynomial programming problems. (C) 2002 Elsevier Science B.V. All rights reserved.
An absolute value representation of continuous piecewise linear functions at high-dimensional space has not been perfectly solved till now. The representation is given by using an iterative method, based on the repres...
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An absolute value representation of continuous piecewise linear functions at high-dimensional space has not been perfectly solved till now. The representation is given by using an iterative method, based on the representation at one-dimensional space. Meanwhile, it is proven that the novel representation is available for all high dimensional continuous piecewise linear functions.
An absolute value representation of continuous piecewise linear functions at high-dimensional space has not been perfectly solved till now. The representation is given by using an iterative method, based on the repres...
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An absolute value representation of continuous piecewise linear functions at high-dimensional space has not been perfectly solved till now. The representation is given by using an iterative method, based on the representation at one-dimensional space. Meanwhile, it is proven that the novel representation is available for all high dimensional continuous piecewise linear functions.
The Choquet and Sugeno (fuzzy) integrals are examples of piecewise linear functions on a finite dimensional space R-n. In this paper we consider piecewise linear functions as aggregation functions and establish a Max-...
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The Choquet and Sugeno (fuzzy) integrals are examples of piecewise linear functions on a finite dimensional space R-n. In this paper we consider piecewise linear functions as aggregation functions and establish a Max-Min polynomial representation of these functions.
The posynomial fractional programming (PFP) problem arises from the summation minimization of several quotient terms, which are composed of posynomial terms appearing in the objective function subject to given posynom...
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The posynomial fractional programming (PFP) problem arises from the summation minimization of several quotient terms, which are composed of posynomial terms appearing in the objective function subject to given posynomial constraints. This paper proposes an approximate approach to solving a PFP problem. A linear programming relaxation is derived for the problem based on piecewiselinearization techniques, which first convert a posynomial term into the sum of absolute terms;these absolute terms are then linearized by some linearization techniques. The proposed approach could reach a solution as close as possible to a global optimum. (C) 2002 Elsevier Science B.V. All rights reserved.
This paper gives a novel generalized absolute value representation of two-dimensional continuous piecewise-linear (PWL) functions, which is obtained by analyzing the fundamental structures of a PWL function instead of...
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ISBN:
(纸本)078037150X
This paper gives a novel generalized absolute value representation of two-dimensional continuous piecewise-linear (PWL) functions, which is obtained by analyzing the fundamental structures of a PWL function instead of its subdomains. The availability of the novel representation is proven.
Continuous piecewise-linear (PWL) functions can be represented by a scheme that selects adequately the linear components of the function without considering explicitly the boundaries. The representation method based o...
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Continuous piecewise-linear (PWL) functions can be represented by a scheme that selects adequately the linear components of the function without considering explicitly the boundaries. The representation method based on the Lattice Theory, that we call the lattice PWL model, is a form that fits that scheme. In this paper, two domain partitions are proposed that give rise to region configurations practically meaningful for the realizability of lattice models. In one of those partitions, each region is uniquely determined by one of the linearfunction. The other region configuration is derived from the rearrangement in ascending order of the linear components. Both configurations are discussed and connected with the domain partition generated by the set of boundaries, frequently considered when dealing with PWL functions. The realization method of lattice models is adapted to the three region configurations, comparing the efficiency of the resulting versions. (C) 1999 Elsevier Science Ltd. All rights reserved.
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