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1
Content available remote On weak sharp minima in vector optimization with applications to parametric problems
100%
Bednarczuk E.
Control and Cybernetics
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2007
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tom Vol. 36, no 3
563-570
EN
In the paper we discuss the concepts of weak sharp solutions to vector optimization problems. As an application we provide sufficient conditions for stability of solutions in perturbed vector optimization problems.
2
Content available remote On stability of some lexicographic multicriteria Boolean problem
100%
Emelichev V. A. , Gurevsky E. E.
Control and Cybernetics
|
2007
|
tom Vol. 36, no 2
333-346
EN
We consider a multicriteria lexicographic Boolean problem of minimizing absolute deviations of linear functions from zero. We investigate the stability radius which can be understood as a limit level of independent perturbations of the parameters, for which new lexicographic optima do not appear. Lower and upper accessible bounds of the stability radius are obtained.
3
Content available remote On the connectivity of efficient point sets
100%
Song W.
Applicationes Mathematicae
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1998-1999
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tom 25
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nr 1
121-127
EN
The connectivity of the efficient point set and of some proper efficient point sets in locally convex spaces is investigated.
4
Content available On lower Lipschitz continuity of minimal points
100%
Bednarczuk E.
|
|
nr 2
245-255
EN
In this paper we investigate the lower Lipschitz continuity of minimal points of an arbitrary set A depending upon a parameter u . Our results are formulated with the help of the modulus of minimality. The crucial requirement which allows us to derive sufficient conditions for lower Lipschitz continuity of minimal points is that the modulus of minimality is at least linear. The obtained results can be directly applied to stability analysis of vector optimization problems.
5
Content available remote Order-Lipschitzian properties of multifunctions with applications to stability of efficient points
88%
Bednarczuk E. M.
Control and Cybernetics
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2003
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tom Vol. 32, no 3
491-502
EN
We define order-Lipschitzian properties of multifunctions and we investigate local upper order-lipschitzness and order-calmness of efficient points of a set depending upon a parameter.
6
Content available Contingent epiderivative and its applications to set-valued optimization
88%
Bednarczuk E. , Song W.
Control and Cybernetics
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1998
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tom Vol. 27, no 3
375-386
EN
In the present paper we give an alternative definition of contingent epiderivative for a set-valued map. We use our concept of contingent epiderivative to formulate necessary and/ or sufficient optimality conditions for a set-valued optimization problem and to study sensivity of a family of parametrized vector optimization problems.
7
Content available Optimality conditions and a classification of duality schemes in vector optimization
75%
El Ghali B.
Control and Cybernetics
|
2000
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tom Vol. 29, no 4
839-860
EN
Vector minimization of a relation F valued in an ordered vector space under a constraint A consists in finding x[0] belongs to A, w[0] belongs to Fx[0] such that w[0] is minimal in FA. To a family of vector minimization problems minimize[x belongs to X] F(x, y), y [belongs to] Y, one associates a Lagrange relation [L(x, [xi], y[0]) = union of sets y belongs to Y(F(x, y)-xi(y)+(y[0]))] where [xi] belongs to an arbitrary class [Xi] of mappings. For this type of problem, there exist several notions of solutions. Some useful characterizations of existential solutions are established and, consequently, some necessary conditions of optimality are derived. One result of intermediate duality is proved with the aid of the scalarization theory. Existence theorems for existential solutions are given and a comparison of several exact duality schemes is established, more precisely in the convex case it is shown that the majority of exact duality schemes can be obtained from one result of S. Dolecki and C. Malivert.
8
Content available remote C^1'1 vector optimization problems and Riemann derivatives
75%
Ginchev I. , Guerraggio A. , Rocca M.
Control and Cybernetics
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2004
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tom Vol. 33, no 2
259-273
EN
In this paper we introduce a generalized second-order Riemann-type derivative for C^1'1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that, these conditions are stronger than those obtained by means of the second-order subdinerential in Clarke sense considered in Guerraggio, Luc (2001) and also to some extent than those obtained in Guerraggio, Luc, Minh (2001).
9
Content available Hoelder-like properties of minimal points in vector optimization
75%
Bednarczuk E.
Control and Cybernetics
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2002
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tom Vol. 31, no 3
423-438
EN
We derive conditions for Hoelder calmness of minimal points of a given set, as a function of a parameter appearing in the description of the set. Different criteria are proved depending on whwther the ordering cone has a nonempty interior or not.
10
Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone
63%
Stasiak A.
Journal of Applied Analysis
|
2018
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tom Vol. 24, nr 1
45--54
EN
Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212-221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.
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