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A Projected Gradient Method for Vector Optimization Problems
Computational Optimization and Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L. Mauricio Graña Drummond +1 more
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Scalarizing vector optimization problems
Journal of Optimization Theory and Applications, 1984A scalarization of vector optimization problems is proposed, where optimality is defined through convex cones. By varying the parameters of the scalar problem, it is possible to find all vector optima from the scalar ones. Moreover, it is shown that, under mild assumptions, the dependence is differentiable for smooth objective maps defined over ...
A. PASCOLETTI, SERAFINI, Paolo
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Vector Variational Inequality and Vector Optimization Problem
1987The theory as well as the application of the variational inequality have been well documented in the literature. In recent years, various extensions of this problems have been proposed and analyzed. Perhaps the most general extension of the variational inequality in the one studied by Giannessi [1].
Guang-Ya Chen, Ging-Min Cheng
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On combinatorial vector optimization problems
Discrete Mathematics and Applications, 1995Summary: A class of combinatorial optimization problems with several criteria of the form MINMAX and MINSUM in arbitrary combinations is investigated. A class of vector optimization problems is formulated in terms of systems of subsets. It contains optimization problems on graphs and Boolean programming.
Emelichev, V. A., Kravtsov, M. K.
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On the reciprocal vector optimization problems
Journal of Optimization Theory and Applications, 1985A necessary and sufficient condition is established for an optimal solution of a primal vector optimization problem to be an optimal solution of its reciprocal. Such a condition is developed and analyzed in the Pareto case, the strong case, and the lexicographic case. We detail these results for ordinary (i.e., scalar) optimization problems.
PAPPALARDO, MASSIMO, FAVATI P.
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Optimality Conditions for Vector Optimization Problems
2014In this chapter we provide subdifferential information for the scalarization functionals introduced in Chap. 6. Based on that we are able to formulate necessary and sufficient optimality conditions of Fermat and Lagrange type for unconstrained and constrained vector optimization problems with (set-valued) objective maps mapping in a real linear space ...
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Scalarization of vector optimization problems
Journal of Optimization Theory and Applications, 1987We investigate the scalar representation of vector optimization problems in close connection with monotonic functions. We show that it is possible to construct linear, convex, and quasiconvex representations for linear, convex, and quasiconvex vector problems, respectively.
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Vector Stochastic Optimization Problems
2001A vector optimization problem is studied, whose objective function is a vector of distribution functions depending on a vector of decision variables. Properties of the model are investigated and a scalar representation in terms of the joint distribution function is proposed.
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