Many problems in the design and implementation of computational schemes may be studied using the theory and methods of mathematical programming. One seeks to minimize bounds for the errors in the calculated results ob...
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Many problems in the design and implementation of computational schemes may be studied using the theory and methods of mathematical programming. One seeks to minimize bounds for the errors in the calculated results obtained from a given set of input data, exploiting analytical relations. We describe optimal quadrature rules and give an application to the evaluation of the sums of power series, belonging to an important class. We present results which are based on the theory of linear and semi-infinite programming. We also study the associated complexity issues and obtain simple qualitative results for the computational work required. (C) 2006 Elsevier B.V. All rights reserved.
作者：
Inuiguchi, MasahiroOsaka Univ
Grad Sch Engn Sci Dept Syst Innovat Div Math Sci Social Syst Toyonaka Osaka 5608531 Japan
In this paper, we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes. The problem is formulated as a necessity measure optimization model. It is shown that ...
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In this paper, we treat fuzzy linear programming problems with uncertain parameters whose ranges are specified as fuzzy polytopes. The problem is formulated as a necessity measure optimization model. It is shown that the problem can be reduced to a semi-infinite programming problem and solved by a combination of a bisection method and a relaxation procedure. An algorithm in which the bisection method and the relaxation procedure converge simultaneously is proposed. A simple numerical example is given to illustrate the solution procedure. (C) 2007 Elsevier B.V. All rights reserved.
We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper as...
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We study a variational inequality problem whose domain is defined by infinitely many linear inequalities. A discretization method and an analytic center based inexact cutting plane method are proposed. Under proper assumptions, the convergence results for both methods are given. We also provide numerical examples to illustrate the proposed methods.
We clarify a financial meaning of duality in the semi-infinite programming problem which emerges in the context of determining a derivative price range based only on the no-arbitrage assumption and the observed prices...
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We clarify a financial meaning of duality in the semi-infinite programming problem which emerges in the context of determining a derivative price range based only on the no-arbitrage assumption and the observed prices of other derivatives. The interpretation links studies in the above context to studies in stochastic models. (c) 2006 Elsevier B.V. All rights reserved.
We deal with two discrete moment problems: first, deciding when a fixed element of R-d is the vector of d first moments for some discrete probability distribution on a given interval [a, b] (feasibility moment problem...
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We deal with two discrete moment problems: first, deciding when a fixed element of R-d is the vector of d first moments for some discrete probability distribution on a given interval [a, b] (feasibility moment problem) and, second, maximizing (minimizing) a given linear combination of moments on the set of discrete probability distributions on [a, b] whose d first moments are given (optimization moment problem). These problems are linked with the cyclic body (which is the union of all cyclic polytopes on [a, b]). The cyclic polytopes have been extensively studied and their combinatorial and geometric properties are noteworthy. The cyclic body also has interesting geometric properties. We totally determine its facial structure and supporting hyperplanes, and we construct an external representation by means of linear inequality systems whose coefficients are symmetric polynomials depending on parameters. These tools allow us to solve the mentioned moment problems by using linear semi-infinite programming, and we obtain a representation of non-negative polynomials over [a, b] as well. (C) 2007 Elsevier Inc. All rights reserved.
This paper addresses the hedging of bond portfolios interest rate risk by drawing on the classical one-period no-arbitrage approach of financial economics. Under quite weak assumptions, several maximin portfolios are ...
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This paper addresses the hedging of bond portfolios interest rate risk by drawing on the classical one-period no-arbitrage approach of financial economics. Under quite weak assumptions, several maximin portfolios are introduced by means of semi-infinite mathematical programming problems. These problems involve several Banach spaces;consequently, infinite-dimensional versions of classical algorithms are required. Furthermore, the corresponding solutions satisfy a saddle-point condition illustrating how they may provide appropriate hedging with respect to the interest rate risk.
This paper deals with the so-called total ill-posedness of linear optimization problems with an arbitrary (possibly infinite) number of constraints. We say that the nominal problem is totally ill-posed if it exhibits ...
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This paper deals with the so-called total ill-posedness of linear optimization problems with an arbitrary (possibly infinite) number of constraints. We say that the nominal problem is totally ill-posed if it exhibits the highest unstability in the sense that arbitrarily small perturbations of the problem's coefficients may provide both, consistent (with feasible solutions) and inconsistent problems, as well as bounded (with finite optimal value) and unbounded problems, and also solvable (with optimal solutions) and unsolvable problems. In this paper we provide sufficient conditions for the total ill-posedness property exclusively in terms of the coefficients of the nominal problem. (C) 2006 Elsevier B.V. All rights reserved.
We present the theoretical background and the numerical procedure for calculating optimum experimental designs for non-linear model discrimination in the presence of constraints. The design support points consist of t...
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We present the theoretical background and the numerical procedure for calculating optimum experimental designs for non-linear model discrimination in the presence of constraints. The design support points consist of two kinds of factors: a continuous function of time and discrete levels of other quantitative factors. That is, some of the experimental conditions are allowed to continually vary during the experimental run. We implement the theory in a chemical kinetic model discrimination problem. (c) 2007 Elsevier B.V. All rights reserved.
In this article, some sensitivity analysis of the dual Optimal value in linear semi-infinite optimization is carried out via the notion of primal/dual asymptotic solution. The sensitivity results are then applied to d...
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In this article, some sensitivity analysis of the dual Optimal value in linear semi-infinite optimization is carried out via the notion of primal/dual asymptotic solution. The sensitivity results are then applied to derive some Hoffman-type inequalities (error bounds). Like in [Renegar, J., 1994, Some perturbation theory for linear programming. mathematical programming, 65A, 73-91], asymptotic solutions also turn out to be a key tool for any sensitivity analysis in the setting of semi-infinite linear duality.
This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right-hand side of the constraints and linear perturbations...
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This paper is concerned with the Lipschitzian behavior of the optimal set of convex semi-infinite optimization problems under continuous perturbations of the right-hand side of the constraints and linear perturbations of the objective function. In this framework we provide a sufficient condition for the metric regularity of the inverse of the optimal set mapping. This condition consists of the Slater constraint qualification, together with a certain additional requirement in the Karush-Kuhn-Tucker conditions. For linear problems this sufficient condition turns out to be also necessary for the metric regularity, and it is equivalent to some well-known stability concepts.
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