We consider linear semi-infinite optimization problems and prove characterizations for strong unicity. One of these is a weak alternation property. This result suggests the introduction of the property of regular stro...
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We consider linear semi-infinite optimization problems and prove characterizations for strong unicity. One of these is a weak alternation property. This result suggests the introduction of the property of regular strong unicity, which is equivalent to a stronger alternation property. The theorems are used in order to prove a Haar-type theorem for linear optimization problems. An application to best Chebyshev approximation is given.
Vector-maximization-problems arise when more than one objective function are to be simultaneously maximized over a feasibility region. The concept of proper efficiency has been introduced by Geoffrion in order to elim...
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Vector-maximization-problems arise when more than one objective function are to be simultaneously maximized over a feasibility region. The concept of proper efficiency has been introduced by Geoffrion in order to eliminate points of a certain anomalous type. In this paper, a generalization is provided for the characterization of the properly efficient solutions, as solutions of some parametric programming problems. A specific characterization is given in the case of bicriterion programs.
In this paper concerned is the stability property of the optimum of nonlinear distribution problems with respect to the random vector. We give conditions, under which the optimum of the problem with approximate random...
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In this paper concerned is the stability property of the optimum of nonlinear distribution problems with respect to the random vector. We give conditions, under which the optimum of the problem with approximate random vectors will converge to the optimum of the original problem in distribution sense, L1-sense or in the sense of mean-convergence respectively. Based upon this stability an approximation method is suggested.
This paper addresses itself to the algorithm for minimizing the sum of a convex function and a product of two linear functions over a polytope. It is shown that this nonconvex minimization problem can be solved by sol...
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In [R. Hettich and P. Zencke, Teubner Studienbücher Mathematik, Leipzig, Stuttgart, 1982] and [G. Speich, Ph.D. thesis, University of Bonn, Bonn, 1981] a Newton-type differential correction algorithm for general ...
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In [R. Hettich and P. Zencke, Teubner Studienbücher Mathematik, Leipzig, Stuttgart, 1982] and [G. Speich, Ph.D. thesis, University of Bonn, Bonn, 1981] a Newton-type differential correction algorithm for general rational Chebyshev approximation has been introduced that has been shown to be globally convergent and superlinearly convergent under assumptions weaker than the common condition of unique solutions. Using recent results on parametric semi-infinite programming [Math. programming, 38 (1987), pp. 323–340], it can be shown that all essential assumptions can be dropped without destroying superlinear convergence. Moreover, additional constraints on the problem, such as restrictions on the range, can be treated without destroying the favorable properties of the algorithm.
Zimmermann's fuzzy approach to the compromise solution concept in the multi-objective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to obj...
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Zimmermann's fuzzy approach to the compromise solution concept in the multi-objective linear programming problem is considered. It is shown that given a class of membership functions of fuzzy goals assigned to objective functions in the problem, wider than primarily proposed by Zimmermann, the use of classical linear programming methods to solve and analyse the problem is also possible. As a result of application of the method based on the parametric programming technique, one can obtain a fuzzy solution of the problem. This solution is a certain fuzzy subset of the set of weakly efficient solutions of the problem. The solution which belongs to this set to the highest degree is a maximizing one (in Bellman and Zadeh's terminology). It may also be obtained by use of the usual non-parametric simplex method.
An algorithm for computing Kuhn-Tucker curves of one-parametric semi-infinite optimization problems p(t), tϵR is presented. Starting witii a Kuhv-Tucker point x for a fixed t an underdetermined system of nonlinear equ...
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In this paper a multiparametric linear fractional functionals program, with parameters appearing only in the objective function, is generated. The optimum solution of this parametric program is supposed to satisfy the...
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