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  • 1
    Electronic Resource
    Electronic Resource
    Theorems of the Alternative and Optimization with Set-Valued Maps (2000)
    Springer
    Journal of optimization theory and applications 107 (2000), S. 627-640 
    Details
    ISSN: 1573-2878
    Keywords: vector optimization ; set-valued maps ; generalized convexity ; equivalent conditions ; theorem of the alternatives ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the concept of generalized cone subconvexlike set-valued mapsis presented and a theorem of alternative for the system of generalizedinequality–equality set-valued maps is established. By applying thetheorem of the alternative and other results, necessary and sufficientoptimality conditions for vector optimization problems with generalizedcone subconvexlike set-valued maps are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1026407517917
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  • 2
    Electronic Resource
    Electronic Resource
    On Vector Variational Inequalities: Application to Vector Equilibria (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 431-443 
    Details
    ISSN: 1573-2878
    Keywords: Vector variational inequalities ; vector optimization ; flow equilibria
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We motivate the study of a vector variational inequality by a practical flow equilibrium problem on a network, namely a generalization of the well-known Wardrop equilibrium principle. Both weak and strong forms of the vector variational inequality are discussed and their relationships to a vector optimization problem are established under various convexity assumptions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022647607947
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  • 3
    Electronic Resource
    Electronic Resource
    Vector Variational Inequality and Vector Pseudolinear Optimization (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 729-734 
    Details
    ISSN: 1573-2878
    Keywords: Vector variational inequalities ; vector optimization ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The study of a vector variational inequality has been advanced because it has many applications in vector optimization problems and vector equilibrium flows. In this paper, we discuss relations between a solution of a vector variational inequality and a Pareto solution or a properly efficient solution of a vector optimization problem. We show that a vector variational inequality is a necessary and sufficient optimality condition for an efficient solution of the vector pseudolinear optimization problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022694427027
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