20 research outputs found

    Decision analysis: vector optimization theory

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    First published in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales in 93, 4, 1999, published by the Real Academia de Ciencias Exactas, Físicas y Naturales

    Necessary and Sufficient Optimality Conditions for Vector Equilibrium Problems on Hadamard Manifolds

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    The aim of this paper is to show the existence and attainability of Karush–Kuhn–Tucker optimality conditions for weakly efficient Pareto points for vector equilibrium problems with the addition of constraints in the novel context of Hadamard manifolds, as opposed to the classical examples of Banach, normed or Hausdorff spaces. More specifically, classical necessary and sufficient conditions for weakly efficient Pareto points to the constrained vector optimization problem are presented. The results described in this article generalize results obtained by Gong (2008) andWei and Gong (2010) and Feng and Qiu (2014) from Hausdorff topological vector spaces, real normed spaces, and real Banach spaces to Hadamard manifolds, respectively. This is done using a notion of Riemannian symmetric spaces of a noncompact type as special Hadarmard manifolds

    Some relations between Minty variational-like inequality problems and vectorial optimization problems in Banach spaces

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    This paper is devoted to the study of relationships between solutions of Stampacchia and Minty vector variational-like inequalities, weak and strong Pareto solutions of vector optimization problems and vector critical points in Banach spaces under pseudo-invexity and pseudo-monotonicity hypotheses. We have extended the results given by Gang and Liu (2008) [22] to Banach spaces and the relationships obtained for weak efficient points in Santos et al. (2008) [21] are completed and enabled to relate vector critical points, weak efficient points, solutions of the Minty and Stampacchia weak vector variationallike inequalities problems and solutions of perturbed vector variational-like inequalities problems

    Local cone approximations in mathematical programming

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    We show how to use intensively local cone approximations to obtain results in some fields of optimization theory as optimality conditions, constraint qualifications, mean value theorems and error bound

    The method of Weighted Multi objective Fractional Linear Programming Problem (MOFLPP)

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    More theories and algorithms in non-linear programming with titles convexity (Convex). When the objective function is fractional function, will not have to have any swelling, but can get other good properties have a role in the development of algorithms decision problem.In this work we focus on the weights method- (one of the classical methods to solve Multi objective convex case problem). Since we have no convex or no concave objective functions, and this condition is essential part on this method implementation, we these valid conditions under method as generator sets efficient and weakly efficient this problem. This raises the need to a detailed study of pseudoconvex idea, cause convex idea, Invex, pseudoinvex idea,…, etc. concepts. Offer a numerical example to show the valid by the conditions previously set generate all weakly efficient set our problem

    Pareto optimality conditions and duality for vector quadratic fractional optimization problems

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    One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.Coordenação de aperfeiçoamento de pessoal de nivel superior (Brasil)Ministerio de Ciencia y TecnologíaConselho Nacional de Desenvolvimento Científico e Tecnológico (Brasil)Fundação de Amparo à Pesquisa do Estado de São Paul

    Well-Behavior, Well-Posedness and Nonsmooth Analysis

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    AMS subject classification: 90C30, 90C33.We survey the relationships between well-posedness and well-behavior. The latter notion means that any critical sequence (xn) of a lower semicontinuous function f on a Banach space is minimizing. Here “critical” means that the remoteness of the subdifferential ∂f(xn) of f at xn (i.e. the distance of 0 to ∂f(xn)) converges to 0. The objective function f is not supposed to be convex or smooth and the subdifferential ∂ is not necessarily the usual Fenchel subdifferential. We are thus led to deal with conditions ensuring that a growth property of the subdifferential (or the derivative) of a function implies a growth property of the function itself. Both qualitative questions and quantitative results are considered
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